Seminario de Sistemas Dinámicos
El Seminario de Sistemas Dinámicos de Santiago es el encuentro semanal de matemáticas con mayor tradición en el país pues se realiza ininterrumpidamente desde la década del '80. Se realiza alternadamente en alguna de las instituciones de Santiago donde hay miembros del grupo de Sistemas Dinámicos. Participan así las universidades de Chile, de Santiago, Andrés Bello y Católica de Chile.
2013-02-21
Renaud Leplaideur. Université de Brest
Construction of explicit examples of diffeomorphisms at the border of the Uniformly hyperbolic ones and Kupka Smale
Sala 1 de la Facultad de Matemáticas UC - 16:30 Hrs.
Abstract:
Resumen: The goal is to construct diffeomorphisms that are not uniformly hyperbolic but such that every periodic point is hyperbolic and stable and unstable manifolds are mutually transverse. In the first part I will present some discussion on what hyperbolic means, and then present the main motivation: to get phase transition for the thermodynamic formalism.
Then, I will present several step of the construction, explaining what are the problems to solve and how we can do it.
"
Construction of explicit examples of diffeomorphisms at the border of the Uniformly hyperbolic ones and Kupka Smale
Sala 1 de la Facultad de Matemáticas UC - 16:30 Hrs.
Abstract:
Resumen: The goal is to construct diffeomorphisms that are not uniformly hyperbolic but such that every periodic point is hyperbolic and stable and unstable manifolds are mutually transverse. In the first part I will present some discussion on what hyperbolic means, and then present the main motivation: to get phase transition for the thermodynamic formalism.
Then, I will present several step of the construction, explaining what are the problems to solve and how we can do it.
"
2013-01-14
Hiroki Takahasi. Tokyo University
Thermodynamic Formalism for The Henon Map At The First Bifurcation
Sala 1 - Facultad de Matemáticas - 16:30 Hrs.
Thermodynamic Formalism for The Henon Map At The First Bifurcation
Sala 1 - Facultad de Matemáticas - 16:30 Hrs.
2012-11-26
Yiwei Zhang. Pontificia Universidad Católica de Chile
On the mixing properties of piecewise expanding maps under composition with permutations (Joint work with Nigel Byott and Mark Holland)
Sala 1 Facultad de Matemáticas PUC
Abstract:
Resumen:
We consider the effect on the mixing properties of a piecewise smooth interval map $f$ when its domain is divided into $N$ equal
subintervals and $f$ is composed with a permutation of these. The case of the stretch-and-fold map $f(x)=mx mod 1$ for integers $m geq 2$is examined in detail. We give a combinatorial description of those permutations $sigma$ for which $sigma circ f$ is still (topologically) mixing, and show that the proportion of such permutations tends to $1$ as $N o infty$. We then investigate the mixing rate of $sigma circ f$ (as measured by the modulus of the second largest eigenvalue of the transfer operator). In contrast to the situation for continuous time diffusive systems, we show that composition with a permutation cannot improve the mixing rate of $f$, but typically makes it worse. Under some mild assumptions on $m$ and $N$, we obtain a precise value for the worst mixing rate as $sigma$ranges through all permutations; this can be made arbitrarily close to $1$ as $N o infty$ (with $m$ fixed). We illustrate the geometric distribution of the second largest eigenvalues in the complex plane for small $m$ and $N$, and propose a conjecture concerning their location in general. Finally, we give examples of other interval maps $f$ for which composition with permutations produces different behavior than that obtained from the stretch-and-fold map.
On the mixing properties of piecewise expanding maps under composition with permutations (Joint work with Nigel Byott and Mark Holland)
Sala 1 Facultad de Matemáticas PUC
Abstract:
Resumen:
We consider the effect on the mixing properties of a piecewise smooth interval map $f$ when its domain is divided into $N$ equal
subintervals and $f$ is composed with a permutation of these. The case of the stretch-and-fold map $f(x)=mx mod 1$ for integers $m geq 2$is examined in detail. We give a combinatorial description of those permutations $sigma$ for which $sigma circ f$ is still (topologically) mixing, and show that the proportion of such permutations tends to $1$ as $N o infty$. We then investigate the mixing rate of $sigma circ f$ (as measured by the modulus of the second largest eigenvalue of the transfer operator). In contrast to the situation for continuous time diffusive systems, we show that composition with a permutation cannot improve the mixing rate of $f$, but typically makes it worse. Under some mild assumptions on $m$ and $N$, we obtain a precise value for the worst mixing rate as $sigma$ranges through all permutations; this can be made arbitrarily close to $1$ as $N o infty$ (with $m$ fixed). We illustrate the geometric distribution of the second largest eigenvalues in the complex plane for small $m$ and $N$, and propose a conjecture concerning their location in general. Finally, we give examples of other interval maps $f$ for which composition with permutations produces different behavior than that obtained from the stretch-and-fold map.
2012-11-19
Pablo Guarino. Usp, Brasil
Rigidez geométrica de homeomorfismos críticos del círculo
Sala 1 de la Facultad de Matemáticas PUC - 16:30 hrs.
Abstract:
Resumen: Hablaremos de homeomorfismos del círculo que están en el borde de los difeomorfismos. Mas explícitamente, estudiaremos
homeomorfismos del círculo de clase C^3 que no son difeomorfismos, pues presentan un punto crítico (de grado impar). Nos concentraremos en el caso de número de rotación irracional de tipo limitado y mostraremos cómo se prueba la siguiente rigidez geométrica: dos homemorfismos críticos con igual número de rotación irracional de tipo limitado e igual grado en el punto crítico son conjugados por un difeomorfismo de clase C^{1+alpha}. Esto surgió como una conjetura a comienzos de los años ´80 a través de trabajos de Feigenbaum, Lanford, Rand, etc. Luego de muchas contribuciones para el caso real-analítico (de Faria-de Melo,
Yampolsky, Khanin-Teplinsky) he
Rigidez geométrica de homeomorfismos críticos del círculo
Sala 1 de la Facultad de Matemáticas PUC - 16:30 hrs.
Abstract:
Resumen: Hablaremos de homeomorfismos del círculo que están en el borde de los difeomorfismos. Mas explícitamente, estudiaremos
homeomorfismos del círculo de clase C^3 que no son difeomorfismos, pues presentan un punto crítico (de grado impar). Nos concentraremos en el caso de número de rotación irracional de tipo limitado y mostraremos cómo se prueba la siguiente rigidez geométrica: dos homemorfismos críticos con igual número de rotación irracional de tipo limitado e igual grado en el punto crítico son conjugados por un difeomorfismo de clase C^{1+alpha}. Esto surgió como una conjetura a comienzos de los años ´80 a través de trabajos de Feigenbaum, Lanford, Rand, etc. Luego de muchas contribuciones para el caso real-analítico (de Faria-de Melo,
Yampolsky, Khanin-Teplinsky) he
2012-10-29
Rafael Tiedra. Pontificia Universidad Católica de Chile
Commutator methods for the spectral analysis of time changes of horocycle flows
Sala 1 de la Facultad de Matemáticas - 16:30 Hrs.
Abstract:
Resumen:
We prove that all time changes of the horocycle flow on compact surfaces of constant negative curvature have purely absolutely continuous spectrum in the orthocomplement of the constant functions. This provides an answer to a question of A. Katok and J.-P. Thouvenot on the spectral nature of time changes of horocycle flows. Our proofs rely on positive commutator methods for self-adjoint operators and the unique ergodicity of the horocycle flow.
Commutator methods for the spectral analysis of time changes of horocycle flows
Sala 1 de la Facultad de Matemáticas - 16:30 Hrs.
Abstract:
Resumen:
We prove that all time changes of the horocycle flow on compact surfaces of constant negative curvature have purely absolutely continuous spectrum in the orthocomplement of the constant functions. This provides an answer to a question of A. Katok and J.-P. Thouvenot on the spectral nature of time changes of horocycle flows. Our proofs rely on positive commutator methods for self-adjoint operators and the unique ergodicity of the horocycle flow.
2012-10-09
Fabio Tal. Universidade de Sao Paulo
Sublinear displacement for conservative
Auditorio del Departamento de Matemática USACH
Abstract:
Resumen: (j.w. with A. Koropecki) In this talk we will consider area preserving homeomorphisms of the 2-torus which are homotopic to the identity and whose rotation set (a concept analogous to the rotation number of a homeomorphisms of the circle) is either a single point or a nondegenerate line segment. Whenever the rotation set of an homeomorphisms consists of a single point $v$, it is called a pseudo-rotation, and these type of maps have been extensively studied in the case where $v$ has an irrational component. On the other hand not much is known when the rotation set of $f$ is reduced to a single point with rational coordinates.
We will show that there exists a pathological example of a smooth homeomorphisms whose rotation set is just the origin, meaning that there exists no point which
Sublinear displacement for conservative
Auditorio del Departamento de Matemática USACH
Abstract:
Resumen: (j.w. with A. Koropecki) In this talk we will consider area preserving homeomorphisms of the 2-torus which are homotopic to the identity and whose rotation set (a concept analogous to the rotation number of a homeomorphisms of the circle) is either a single point or a nondegenerate line segment. Whenever the rotation set of an homeomorphisms consists of a single point $v$, it is called a pseudo-rotation, and these type of maps have been extensively studied in the case where $v$ has an irrational component. On the other hand not much is known when the rotation set of $f$ is reduced to a single point with rational coordinates.
We will show that there exists a pathological example of a smooth homeomorphisms whose rotation set is just the origin, meaning that there exists no point which
2012-10-08
Fabio Tal. Universidade de Sao Paulo
Essential dynamics for surface homeomorphisms
Auditorio del Departamento de Matemática USACH - 16:30 Hrs.
Abstract:
Resumen: (j.w. with A. Koropecki) We will discuss nonwandering homeomorphisms of closed surfaces of genus g which are homotopic to the identity, and we will try to determine when the dynamic of the homeomorphisms is intrinsic to the surface. This means, loosely speaking, that the dynamics cannot be seen as that of an homeomorphisms of a surface with strictly smaller genus.
The main result we obtain is that, if the set of fixed points of the homeomorphism $f$ homotopic to the identity is not essential, then any $f$ invariant open topological disk lifts to a bounded set in the universal covering. We will also discuss 2 consequences of this result, the first one being that the set of essential" points of the dynamic (those point whose orbit of any neighborhood is not homotopically trivial) is itself essential large.
For the specific case of the torus, we show that if the rotation set of $f$ has nonempty interior, then it is possible to partition the torus into 2 different regions, a chaotic one which is externally transitive and realizes all of the rotational dynamics, and an inessential one, consisting of bounded periodic topological disks.
"
Essential dynamics for surface homeomorphisms
Auditorio del Departamento de Matemática USACH - 16:30 Hrs.
Abstract:
Resumen: (j.w. with A. Koropecki) We will discuss nonwandering homeomorphisms of closed surfaces of genus g which are homotopic to the identity, and we will try to determine when the dynamic of the homeomorphisms is intrinsic to the surface. This means, loosely speaking, that the dynamics cannot be seen as that of an homeomorphisms of a surface with strictly smaller genus.
The main result we obtain is that, if the set of fixed points of the homeomorphism $f$ homotopic to the identity is not essential, then any $f$ invariant open topological disk lifts to a bounded set in the universal covering. We will also discuss 2 consequences of this result, the first one being that the set of essential" points of the dynamic (those point whose orbit of any neighborhood is not homotopically trivial) is itself essential large.
For the specific case of the torus, we show that if the rotation set of $f$ has nonempty interior, then it is possible to partition the torus into 2 different regions, a chaotic one which is externally transitive and realizes all of the rotational dynamics, and an inessential one, consisting of bounded periodic topological disks.
"
2012-10-01
Mickaël Crampon. Universidad de Santiago de Chile
El flujo geodésico de los convexos divisibles
Auditorio del Departamento de Matemática - USACH - 16:30 Hrs.
Abstract:
Un convexo divisible es un abierto convexo del espacio proyectivo que admite un cuociente compacto por un subgrupo discreto de transformaciones proyectivas. Cuando el grupo no tiene torsión, el cuociente es una variedad, que admite una métrica natural llamado métrica de Hilbert. De forma general, nos proponemos estudiar el flujo geodésico de esta métrica.
Yves Benoist mostro que mucho depende de si el convexo es estrictamente convexo o no. Si lo es, se puede decir muchas cosas sobre la dinámica del flujo geodesico y recordaré los resultados principales. Si no, no se sabe casi nada. Presentaré en este caso lo que se sabe de la geometria de estas variedades en dimension 3. Luego, introduciré varias preguntas respecto a las propiedades estadísticas del flujo geodésic
El flujo geodésico de los convexos divisibles
Auditorio del Departamento de Matemática - USACH - 16:30 Hrs.
Abstract:
Un convexo divisible es un abierto convexo del espacio proyectivo que admite un cuociente compacto por un subgrupo discreto de transformaciones proyectivas. Cuando el grupo no tiene torsión, el cuociente es una variedad, que admite una métrica natural llamado métrica de Hilbert. De forma general, nos proponemos estudiar el flujo geodésico de esta métrica.
Yves Benoist mostro que mucho depende de si el convexo es estrictamente convexo o no. Si lo es, se puede decir muchas cosas sobre la dinámica del flujo geodesico y recordaré los resultados principales. Si no, no se sabe casi nada. Presentaré en este caso lo que se sabe de la geometria de estas variedades en dimension 3. Luego, introduciré varias preguntas respecto a las propiedades estadísticas del flujo geodésic
2012-09-03
Michal Szostakiewicz. Varsovia
Statistical properties of rational maps: introduction
Sala 1 Facultad de Matemáticas - PUC 15:30 a 16:30 Hrs.
Abstract:
I will explain some basic properties of rational maps on the Riemann Sphere from a dynamic point of view and present a list of known results concerning their statistical properties.
After short geometric introduction, I want to focus on describing Perron-Frobenius operator and using it to construct equilibrium states with Holder continous potential in this setting.
I will also connect convergence of this operator with the statistical properties of the map. I will mention the known results about this convergence and say something about techniques of proving them. If I have time, I will tell more about Young´s towers.
This talk will serve as an introduction to the mini-course with the same name.
Statistical properties of rational maps: introduction
Sala 1 Facultad de Matemáticas - PUC 15:30 a 16:30 Hrs.
Abstract:
I will explain some basic properties of rational maps on the Riemann Sphere from a dynamic point of view and present a list of known results concerning their statistical properties.
After short geometric introduction, I want to focus on describing Perron-Frobenius operator and using it to construct equilibrium states with Holder continous potential in this setting.
I will also connect convergence of this operator with the statistical properties of the map. I will mention the known results about this convergence and say something about techniques of proving them. If I have time, I will tell more about Young´s towers.
This talk will serve as an introduction to the mini-course with the same name.
2012-08-27
Martin Andersson. Uff-Niteroi
Comportamiento ergódico extraño en el mundo C^0 genérico
Auditorio del Depto. de Matemática USACH
Abstract:
Resumen:
Voy a exponer algunos temas de la teoría ergódica de sistemas C^0 genéricos. Lo más notable, en este contexto, es un resultado de la existencia q.t.p. de promedios de Birkhoff y la sorprendente falta de medidas físicas.
En colaboración con Flávio Abdenur.
Comportamiento ergódico extraño en el mundo C^0 genérico
Auditorio del Depto. de Matemática USACH
Abstract:
Resumen:
Voy a exponer algunos temas de la teoría ergódica de sistemas C^0 genéricos. Lo más notable, en este contexto, es un resultado de la existencia q.t.p. de promedios de Birkhoff y la sorprendente falta de medidas físicas.
En colaboración con Flávio Abdenur.
2012-08-20
Jimena Royo-Letelier. Université de Versailles Saint-Quentin-En-Yvelines, France
Two-component Bose-Einstein Condensates
Sala 1 de la Facultad de Matemáticas PUC - 16:30
Abstract:
We deal with minimizers of the coupled Gross-Pitaevskii energy of a two-component Bose-Einstein condensate. We will show the links between our model and other mathematical problems : optimal partition problems and the Cahn-Hilliard model for phase transitions. These links appear in our model in the limit strongly repulsive limit, so the two components segregate. We show that in the weakly interacting regime, the minimal configuration of the segregated minimizers is two half-planes.
Two-component Bose-Einstein Condensates
Sala 1 de la Facultad de Matemáticas PUC - 16:30
Abstract:
We deal with minimizers of the coupled Gross-Pitaevskii energy of a two-component Bose-Einstein condensate. We will show the links between our model and other mathematical problems : optimal partition problems and the Cahn-Hilliard model for phase transitions. These links appear in our model in the limit strongly repulsive limit, so the two components segregate. We show that in the weakly interacting regime, the minimal configuration of the segregated minimizers is two half-planes.
2012-05-28
Sandro Vaienti. Centre de Physique Théorique (Marseille)
Escape Rates Formulae and Metastablilty for Randomly perturbed maps
Sala 1, Facultad de Matemáticas - PUC 16:30 Hrs.
Abstract:
Resumen:
(Joint with W Bahsoun) We provide escape rates formulae for piecewise expanding interval maps with `random holes´. Then we obtain rigorous approximations of invariant densties of randomly perturbed metabstable interval maps. We show that our escape rates formulae can be used to approximate limits of invariant densities of randomly perturbed metastable systems.
Escape Rates Formulae and Metastablilty for Randomly perturbed maps
Sala 1, Facultad de Matemáticas - PUC 16:30 Hrs.
Abstract:
Resumen:
(Joint with W Bahsoun) We provide escape rates formulae for piecewise expanding interval maps with `random holes´. Then we obtain rigorous approximations of invariant densties of randomly perturbed metabstable interval maps. We show that our escape rates formulae can be used to approximate limits of invariant densities of randomly perturbed metastable systems.
2012-05-14
Radu Saghin. Puc-Valparaíso
Volume growth and entropy for partially hyperbolic diffeomorphisms
USACH (sala por confirmar)
Abstract:
Resumen: I will present an inequality between the metric entropy, Lyapunov exponents, and an invariant measuring the growth of the volume in the direction of the unstable foliation (the integrated volume growth of $W^u$) of a $C^1$ partially hyperbolic diffeomorphism. I will discuss some situations where this integrated volume growth is locally constant, and several applications.
Volume growth and entropy for partially hyperbolic diffeomorphisms
USACH (sala por confirmar)
Abstract:
Resumen: I will present an inequality between the metric entropy, Lyapunov exponents, and an invariant measuring the growth of the volume in the direction of the unstable foliation (the integrated volume growth of $W^u$) of a $C^1$ partially hyperbolic diffeomorphism. I will discuss some situations where this integrated volume growth is locally constant, and several applications.
2012-05-07
Daniel Coronel. Pontificia Universidad Católica de Chile
Low-temperature phase transitions in the quadratic family
Sala 403 del edificio R5 (República 399, 4to. piso), UNAB
Abstract:
We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function.
This implies that several dimension spectra and large deviation rate functions associated to this map are not (expected to be) real analytic, in contrast to the uniformly hyperbolic case. The quadratic map we study has a non-recurrent critical point, so it is
non-uniformly hyperbolic in a strong sense. Joint work with Juan Rivera-Letelier.
Low-temperature phase transitions in the quadratic family
Sala 403 del edificio R5 (República 399, 4to. piso), UNAB
Abstract:
We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function.
This implies that several dimension spectra and large deviation rate functions associated to this map are not (expected to be) real analytic, in contrast to the uniformly hyperbolic case. The quadratic map we study has a non-recurrent critical point, so it is
non-uniformly hyperbolic in a strong sense. Joint work with Juan Rivera-Letelier.
2012-03-05
Mike Todd. University of St. Andrews (Escocia)
Transience in Dynamical Systems
Sala 1, facultad de Matematicas, PUC
Transience in Dynamical Systems
Sala 1, facultad de Matematicas, PUC
2012-01-23
Renaud Leplaideur. Université de Brest, Francia
Some advances on the selection problem
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas UC- 16:30 Hrs.
Abstract:
I will present the problem of selection at temperature zero. Given a Dynamical System $X$ and $f o X$ and a potential $phi$ we look for the $f$-invariant measures $mu$ which maximize $int phi,dmu$. Such a measure is called a $phi$-maximizing measure. On the other hand, the Thermodynamical formalism produces an Equilibrium State $mu_eta$ for the potential $etaphi$ with $eta>0$. A ground state for $phi$ is a $phi$-maximizing measure which is an accumulation point for $mu_eta$ as $eta$ goes to $+infty$. The selection problem is to determine if $mu_eta$ converges, and also how it chooses the limit between all the $phi$-maximizing measures. The convergence does not always occur, but it turns out that fore some potentials, it is possible to prove convergence and to determine the limit. The talk will recall part of the background needed to understand and present the problem and will show some results. In particular, we emphasize that the Max-Plus formalism seems to be a powerful tool to solve the problem.
Some advances on the selection problem
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas UC- 16:30 Hrs.
Abstract:
I will present the problem of selection at temperature zero. Given a Dynamical System $X$ and $f o X$ and a potential $phi$ we look for the $f$-invariant measures $mu$ which maximize $int phi,dmu$. Such a measure is called a $phi$-maximizing measure. On the other hand, the Thermodynamical formalism produces an Equilibrium State $mu_eta$ for the potential $etaphi$ with $eta>0$. A ground state for $phi$ is a $phi$-maximizing measure which is an accumulation point for $mu_eta$ as $eta$ goes to $+infty$. The selection problem is to determine if $mu_eta$ converges, and also how it chooses the limit between all the $phi$-maximizing measures. The convergence does not always occur, but it turns out that fore some potentials, it is possible to prove convergence and to determine the limit. The talk will recall part of the background needed to understand and present the problem and will show some results. In particular, we emphasize that the Max-Plus formalism seems to be a powerful tool to solve the problem.
2011-09-26
Francisco Valenzuela. Puc-Valparaíso
Descomposición dominada y puntos críticos
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas - 16.30 hrs
Abstract:
Introducimos el concepto de punto crítico para un cociclo lineal 2-dimensional, y mostramos que la existencia de puntos críticos es la única obstrucción para que el cociclo tenga descomposición dominada.
Descomposición dominada y puntos críticos
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas - 16.30 hrs
Abstract:
Introducimos el concepto de punto crítico para un cociclo lineal 2-dimensional, y mostramos que la existencia de puntos críticos es la única obstrucción para que el cociclo tenga descomposición dominada.
2011-09-12
Alma Armijo. Ufrj Brasil
Entropía Expansiva y Descomposición Dominada
Sala 2 (Víctor Ochsenius) - 16.30 hrs.
Entropía Expansiva y Descomposición Dominada
Sala 2 (Víctor Ochsenius) - 16.30 hrs.
2011-08-07
Thomas Jordan. University of Bristol (Uk).
Self-affine sets
Sala 2 (Víctor Ochsenius) Fac. de Matemáticas PUC
Abstract:
El Seminario Conjunto de Sistemas Dinámicos de este lunes 8 de agosto de 2011 será la primera de tres sesiones de un mini-curso que se realizará durante la semana. Los datos precisos son:
Expositor: Thomas Jordan, University of Bristol (UK).
Título: Self-affine sets.
Hora y lugar: Lunes 8 de agosto a las 16.30 hrs, Sala 2 (Víctor Ochsenius) Fac. de Matemáticas PUC.
Las dos sesiones siguientes se llevarán a cabo en las fechas:
Martes 9 de agosto de 2011, 16:30 hrs. Sala 1 de la Fac. de Matemáticas PUC.
Miércoles 10 de agosto de 2011, 17:00 hrs. Sala 1 de la Fac. de Matemáticas PUC.
"
Self-affine sets
Sala 2 (Víctor Ochsenius) Fac. de Matemáticas PUC
Abstract:
El Seminario Conjunto de Sistemas Dinámicos de este lunes 8 de agosto de 2011 será la primera de tres sesiones de un mini-curso que se realizará durante la semana. Los datos precisos son:
Expositor: Thomas Jordan, University of Bristol (UK).
Título: Self-affine sets.
Hora y lugar: Lunes 8 de agosto a las 16.30 hrs, Sala 2 (Víctor Ochsenius) Fac. de Matemáticas PUC.
Las dos sesiones siguientes se llevarán a cabo en las fechas:
Martes 9 de agosto de 2011, 16:30 hrs. Sala 1 de la Fac. de Matemáticas PUC.
Miércoles 10 de agosto de 2011, 17:00 hrs. Sala 1 de la Fac. de Matemáticas PUC.
"
2011-06-12
Jean-Baptiste Bardet. Lmrs, Université de Rouen & Cmm, Universidad de Chile
Phase transition for a model of globally coupled chaotic interval maps
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas PUC
Abstract:
In a joint work with Gerhard Keller and Roland Zweimüller, we introduce a model of globally coupled chaotic interval maps for
which the self-consistent Perron-Frobenius operator describing the infinite-size dynamics exhibits a bifurcation from a unique stable equilibrium to the coexistence of two stable and one unstable equilibrium, whereas all finite-size dynamics remain chaotic.
Phase transition for a model of globally coupled chaotic interval maps
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas PUC
Abstract:
In a joint work with Gerhard Keller and Roland Zweimüller, we introduce a model of globally coupled chaotic interval maps for
which the self-consistent Perron-Frobenius operator describing the infinite-size dynamics exhibits a bifurcation from a unique stable equilibrium to the coexistence of two stable and one unstable equilibrium, whereas all finite-size dynamics remain chaotic.
Contáctenos
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