Godofredo Iommi
I am a professor at the Facultad de Matemáticas of Pontificia Universidad Católica de Chile. I am also a member of the Chilean research group on Dynamical Systems. A programme of the dynamical systems seminar of Santiago can be found here. My main interests are Ergodic Theory, Dimension Theory and Dynamical Systems.
Office: 308
Email: giommi (at) mat.uc.cl
Papers and Preprints
Odometers, Backward continued fractions and counting rationals. (with Mario Ponce).
Hölder continuity of measures for heavy tail potentials (with Dalia Terhesiu and Mike Todd).
The Halász-Székely barycenter (with Jairo Bochi and Mario Ponce). Proc. Edinburgh Math. Soc. (2) 65, no.4, 881-911 (2022)
Differentiability of the pressure in non-compact spaces (with Mike Todd). Fundamenta Mathematicae 259, Vol.2 151--177 (2022).
Perfect Matchings in Inhomogeneous Random Bipartite Graphs in Random Enviroment. (with Jairo Bochi and Mario Ponce) CUBO 24. no 2. 263-272 (2022).
Escape of entropy for countable Markov shifts. (with Mike Todd and Aníbal Velozo). Advances in Mathematics 405, Paper No. 108507 (2022).
The space of invariant measures for countable Markov shifts (with Anibal Velozo). Journal d'Analyse Mathematique 143 no.2 461-501 (2021).
Pressure, Poincaré series and box dimension of the boundary (with Aníbal Velozo). Nonlinearity 34 no 6. 3936-3952 (2021).
Measures of maximal entropy for suspension flows. (with Aníbal Velozo) Math. Z. 297, no 3-4, 1473-1482 (2021).
Upper semi-continuity of entropy in non-compact settings (with Mike Todd and Aníbal Velozo). Mathematical Research Letters 27. 1055-1077 (2020).
Hidden Gibbs measures on shift spaces over countable alphabtes (with Camilo Lacalle and Yuki Yayama). Stochastics and Dynamics 20, no 4, 2050028 (2020).
Time changes for flows and thermodynamic formalism (with Italo Cipriano). Nonlinearity 32. 2848-2874 (2019).
Entropy in the cusp and phase transitions for geodesic flows (with Felipe Riquelme and Aníbal Velozo) Israel Journal of Mathematics 225. no 2, 609-659 (2018).
Weak Gibbs measures as Gibbs measures for asymptotically additive sequences (with Yuki Yayama). Proceedings of the AMS 145, no 4. 1599-1614 (2017).
Transience and multifractal analysis (with Thomas Jordan and Mike Todd ). Annales de l'Institut Henri Poincare / Analyse non lineaire 34. no 2, 407-421 (2017).
The scaling mean and a law of large permanents (with Jairo Bochi and Mario Ponce). Advances in Mathematics 292, 374-409 (2016).
Recurrence and transience for suspension flows (with Thomas Jordan and Mike Todd). Israel Journal of Mathematics vol. 209, Issue 2, 547–592 (2015).
Multifractal analysis of Birkhoff averages for countable Markov maps (with Thomas Jordan) Ergodic Theory and Dynam. Systems vol. 35, no 08, 2559-2586 (2015).
Multifractal analysis of quotients of Birkhoff sums for countable Markov maps (with Thomas Jordan) Int. Math. Res. Not. IMRN 2, 460-498 (2015).
Zero temperature limits of Gibbs states for almost-additive potentials (with Yuki Yayama) Journal of Statistical Physics 155, 23-46 (2014).
Thermodynamic formalism for interval maps: inducing schemes (with Mike Todd) Dyn. Sys. Issue edited by Quas and Vaienti. vol. 28 Issue 3, 354-380 (2013).
Transience in dynamical systems (with Mike Todd). Ergodic Theory and Dynam. Systems vol 33, no 5, 1450-1476 (2013).
Phase transitions for suspension flows (with Thomas Jordan) Communications in Mathematical Physics 320, 475-498 (2013).
The Lyapunov spectrum as the Newton method. Physica A, 391, vol.9 2848-2852 (2012).
Almost-additive thermodynamic formalism for countable Markov shifts (with Yuki Yayama). Nonlinearity 25, 165-191 (2012).
Dimension theory for multimodal maps (with Mike Todd ). Annales Henri Poincaré 12, 591-620 (2011).
Multifractal analysis and phase transitions for hyperbolic and parabolic horseshoes (with Luis Barreira). Israel Journal of Mathematics vol.181 347--379 (2011).
Natural equilibrium states for multimodal maps (with Mike Todd). Communications in Mathematical Physics 300, 65-94 (2010).
Multifractal analysis of Lyapunov exponent for the backward continued fraction map. Ergodic Theory and Dynam. Systems vol. 30 no.1 211-232 (2010).
The Lyapunov spectrum is not always concave (with Jan Kiwi ) Journal of Statistical Physics vol.135 no.3, 535-546 (2009).
The frequency of digits in the Lüroth expansion (with Luis Barreira) Journal of Number Theory vol. 129 no.6, 1479-1490 (2009). Corrections
Partial quotients of continued fractions and beta-shifts (with Luis Barreira) Nonlinearity 21, 2211-2219 (2008).
Ergodic Optimization for Renewal type shifts Monatshefte fur Mathematik vol.150 no.2, 91-95 (2007).
Multifractal Analysis for the Exponential family (with B. Skorulski) Discrete and Continuous Dynamical Systems vol.16 no.4, 857-869 (2006).
Suspension flows over countable Markov shifts (with Luis Barreira) Journal of Statistical Physics vol.124 no.1, 207-230 (2006).
Multifractal Analysis for countable Markov shifts Ergodic Theory and Dynam. Systems vol. 25 no. 6, 1881-1907 (2005).
Notes
An ergodic theorem for permanents of oblong matrices (with Jairo Bochi and Mario Ponce). (2015) (After the completion of this paper, we were informed that Theorem 1 is a particular case of Theorem U in J. Aaronson, R. Burton, H. Dehling, D. Gilat, T. Hill, B. Weiss. "Strong laws for L– and U–statistics." Trans. Amer. Math. Soc. 348 (1996), no. 7, 2845–2866.).
The Besicovitch formula (2012).
Thermodynamic formalism for the positive geodesic flow on the modular surface. (Superceded by "Phase transitions for suspension flows"by Iommi and Jordan).
Funciones continuas con máximos locales densos Revista del Jóven Matemático no.3, 27-34 (2012) (in Spanish).
The dimension theory of number theoretically defined sets Notes from Encuentro SOMACHI 2008, Valparaíso, 2008.
The Bowen Formula: Dimension Theory and Thermodynamic Formalism Notes from VII Escuela de Sistemas Dinámicos, Valparaíso, 2008.
Lecture Notes
The Mean, the maximal and the pointwise ergodic theorems. (2021).
Cálculo Real. (2014) Lecture notes for the courses of calculus and analysis in one variable (in Spanish).