Samuel Senti

EQUILIBRIUM MEASURES FOR MAPS WITH INDUCING SCHEMES

We introducea class of continuousmaps f of a compact topologi- cal space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamicformalism, i.e., de- scribe a class of real-valued potential functions ϕ on I, which admit a unique equilibrium measure ¹ ϕ minimizing the free energy for a certain class of in- variant measures. We also describe ergodic properties of equilibrium mea- sures, including decay of correlation and the Central Limit Theorem. Our re- sults apply to certain maps of the interval with critical points and/or singular- ities (including some unimodal and multimodal maps) and to potential func- tions ϕt =−t log|d f | with t ∈(t0,t1) for some t0 < 1< t1. In theparticularcase of S-unimodal maps we show that one can choose t0 < 0 and that the class of measures under consideration consists of all invariant Borel probability mea- sures.

Thermodynamics of towers of hyperbolic type

We introduce a class of continuous maps

Lifting measures to inducing schemes

f

Equilibrium measures for the Hénon map at the first bifurcation

of a compact topological space

Thermodynamics of the Katok map

X

Lindeberg theorem for Gibbs–Markov dynamics

admitting inducing schemes of hyperbolic type and describe the associated tower constructions. We then establish a thermodynamic formalism, i.e., we describe a class of real-valued potential functions

Thermodynamical Formalism Associated with Inducing Schemes for One-dimensional Maps

\varphi

Equilibrium measures for the Hénon map at the first bifurcation: Uniqueness and geometric/statistical properties

on

Dimension of weakly expanding points for quadratic maps

X

Maximal entropy measures for Viana maps

such that