2009-11-02

Peter Haissinsky. Marseillle
A notion of invariant line fields for coarse conformal dynamical systems
Sala 2 (Víctor Ochsenius) - 16:30 Hrs. Facultad de Matemáticas - UC
Abstract:
We will focus on the dynamics of finite branched coverings of
the two-sphere which preserve a coarse conformal structure. We will
develop a notion of invariant line fields in this context which will
enable us to characterize those maps which admit optimal metrics (in the
sense of Hausdorff dimension)

2009-10-26

Milton Cobo, Ufes-Brazil. Ufes-Brazil.
Carlos Gutierrez and injectivity of planar maps
CMM UdeChile (7mo piso), 17.00 hrs
Abstract:
Resumen: C. Gutierrez proved, in 1995, the ``global asymptotic conjecture in dimension 2:
If $X:R^2 mapsto R^2$ is a $C^1$ vector field with $X(0)=0$ and such that, for all $pinR^2$, the eigenvalues of the derivative $DX_p$ have negative real part, then $(0,0)$ is a global attractor of the dynamical system ( dot{x} = X(x). )

In this lecture we will present a series of elegant results on injectivity of planar maps $X:R^2 mapsto R^2$,
obtained by Gutierrez, and which provide a simple proof of this conjecture. This lecture is a small tribute to Prof. Gutierrez who
passed away last year."

2009-10-19

Eugenio Trucco. Pontificia Universidad Católica de Chile
Componentes de Fatou Errantes y Conjuntos de Julia Algebraicos
Sala 2 (Víctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:
Dado un polinomio $P$ con coeficientes en $L,$ la completacion del cuerpo de series formales de Puiseux, estudiaremos la acción de $P,$ como sistema dinámico, en la linea afín de Berkovich asociada a $L$. Probaremos que toda componente errante del conjunto de Fatou esta contenida en la cuenca de atracción de una orbita periódica, Esto es, un análogo del Teorema de Sullivan
sobre dominios errantes. Mostraremos que la parte emph{no clásica} del conjunto de Julia de $P$ consiste de un numero finito de grandes orbitas de puntos periódicos. Además, daremos una caracterización de los polinomios cuyo conjunto de Julia es emph{algebraico.}

2009-10-05

Hector Hardy Pastén. Universidad de Concepción
El Problema de Büchi y el Decimo Problema de Hilbert Para Funciones Meromorfas P-Adicas
Sala 2 (Víctor Ochsenius) Facultad de Matemáticas PUC - 16:30 Hrs.

2009-09-21

Gonzalo Contreras. Cimat México
Minicurso Dinámica Lagrangeana
Sala 3 (sector postgrado) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:
Las siguientes sesiones se realizarán los días 23, 25, 28 y 30 de septiembre en el mismo lugar y a la misma hora."

2009-09-14

Daniel Smania. Icmc-Usp (San Carlos), Brasil
On infinitely cohomologous to zero observables
Sala 2 (Víctor Ochsenius)- Facultad de Matemáticas PUC.
Abstract:
Resumen: We show that for a large class of piecewise expanding maps
T, the bounded p-variation observables u_0 that admits an infinite
sequence of bounded p-variation observables u_i satisfying u_i(x)=
u_{i+1}(Tx) -u_{i+1}(x) are constant. The method of the proof consists
in to find a suitable Hilbert basis for L^2(hm), where hm is the
unique absolutely continuous invariant probability of T. In terms of
this basis, the action of the Perron-Frobenious and the Koopan
operator on L^2(hm) can be easily understood. This result generalizes
earlier results by Bamon, Kiwi, Rivera-Letelier and Urzua in the case
T(x)= n x mod 1, n in N-{0,1} and Lipchitizian observables u_0. This a
joint work with Amanda de Lima.

2009-08-26

Laurent Bartholdi. University de Göttingen
Insanely Twisted Rabbits
Sala 3 (sector postgrado) Facultad de Matemáticas de la PUC.

2009-08-24

Helge Gloeckner. Universitat Paderborn
Invariant manifolds for ultrametric dynamical systems and applications in Lie theory
Sala 2 (Víctor Ochsenius), Facultad de Matemáticas - UC. 16:00 Hrs.
Abstract:
Resumen:
Consider a diffeomorphism f: M-> M of a manifold M over a complete ultrametric field (like the p-adic numbers)
and a fixed point, x, of f. Then one can construct the usual types of invariant manifolds around x, as familiar
from the case of manifolds over the real numbers. These studies were motivated by questions concerning Lie groups
over local fields. They allow results to be extended to the case of Lie groups over local fields of positive characteristic,
which previously were only known in the case of zero characteristic (i.e., only for p-adic Lie groups).

2009-08-24

Mike Todd. Universidade Do Porto.
Recurrence and Extreme Value Theory in Dynamical System
Sala 2 (Víctor Ochsenius), Facultad de Matemáticas - UC 17:15 Hrs.

2009-08-17

Alejandro Maass. Dim-Cmm U de Chile
A structure theorem in topological dynamics and applications to nilsequences and maximal nilfactors
Sala múltiple B del CENI-USACH
Abstract:
Resumen: In this talk we present a characterization of (inverse limits of) nilsystems of any order by introduciong the notion of
dynamical parallelepiped. This characterization is used to give a (kind of) local characterization of nilsequences and provide a way to construct maximal nilfactors of a topological dynamical systems in the espirit of the structure theorem by Host and Kra used to prove non conventional ergodic theorems in measurable dynamics.

2009-08-10

Michael Schraudner. Cmm-Udechile
Projectional entropy of multidimensional shifts.
Sala de Seminarios 7mo piso del CMM-UdeChile
Abstract:
Resumen:
We define the projectional entropy of multidimensional shifts with respect to any lower-dimensional sublattice and investigate under which conditions this quantity equals the topological entropy of the original shift. Constructing a three dimensional shift of finite type which satisfies a uniform mixing condition we exhibit a subtle difference between the results for one-dimensional and higher-dimensional sublattices.

The presented results are contained in a paper recently accepted for publication in Discrete and Continuous Dynamical Systems which is also available from my web-page.

2009-07-20

Thomas Jordan. University of Warwick
Hausdorff Dimension of Projections of Self-Affine Carpets.
Sala 2 (Víctor Ochsenius) - 16:00 Hrs. Facultad de Matemáticas - UC

2009-06-08

Feliks Przytycki. Impan Polonia
On The Hausdorff Dimension Spectrum for Characteristic Lyapunov Exponents for Iteration of Rational Maps on The Riemann Sphere
Sala 2 (Víctor Ochsenius) - 16:30 Hrs. Facultad de Matemáticas - UC

2009-06-01

Jan Kiwi, PUC. Pontificia Universidad Católica de Chile
Dinámica Compleja y Dinámica Sobre el Cuerpo de Series de Puiseux: Aplicaciones Racionales Cuadráticas
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.

2009-05-25

Andres Navas. Universidad de Santiago de Chile
Como Ordenar Trenzas
USACH - Sala por confirmar

2009-05-11

Juan Rivera Letelier. Pontificia Universidad Católica de Chile
Statistical properties of real and complex one-dimensional dynamical systems
Sala 2 (Vìctor Ochsenius) - Facultad de Matemáticas - 16:30 Hrs.
Abstract:

"				

2009-04-27

Carlos Vasquez. Universidad Católica de Valparaiso
Sobre la abundancia de medidas físicas para difeomorfismosparcialmente hiperbólicos
USACH, sala por avisar.
Abstract: