August 20th, 2018
Facultad de Matemáticas, UC, Santiago
Tha aim is of this is meeting is twofold, on the one hand we will gather a group of dynamicists to discuss new developments in the area and on the other we will have the Master´s defense of Alexis Moraga
1. Mike Todd (University of St Andrews, United Kingdom).
Title: Phase transitions and limit laws
Abstract: The `statistics’ of a dynamical system is the collection of statistical limit laws it satisfies. This starts with Birkhoff’s Ergodic Theorem, which is about averages of some observable along orbits: this is a pointwise result, for typical points for a given invariant measure. Then we can look for forms of Central Limit Theorem, Large Deviations and so on: these are about how averages fluctuate, globally, with respect to the invariant measure. In this talk I’ll show how the form of the `pressure function´ for a dynamical system determines its statistical limit laws. This is particularly interesting when the system has slow mixing properties, or, even more extreme, in the null recurrent case (where the relevant invariant measure is infinite). I’ll start by introducing these ideas for simple interval maps with nice Gibbs measures and then indicate how this generalises. This is joint work with Henk Bruin and Dalia Terhesiu.
2. Alejandro Kocsard (Universidade Federal Fluminense, Brazil).
Título: Cociclos sobre dinámicas hiperbólicas, exponentes de Lyapunov y
enfoque y algunas aplicaciones.
3. Alexis Moraga (Pontificia Universidad católica de Chile)
Title: Cohomology Equation for isometries of Gromov Hyperbolic spaces
This event is supported by CONICYT through the proyecto Anillo ACT172001, «New trends in Ergodic Theory» and by the Facultad de Matremáticas, Pontificia Universidad Católica de Chile