Equilibrium states for a class of non-uniformly hyperbolic maps

Date. December 04, 14h00m (UTC/GMT)

Speaker.  Jaqueline Siqueira (Universidade Federal do Rio de Janeiro)

Title. Equilibrium states for a class of non-uniformly hyperbolic maps

Abstract.

We consider a wide family of non-uniformly hyperbolic maps and hyperbolic potentials and prove that the unique equilibrium state associated to each element of the family is given by the eigenmeasure and the eigenfunction of the transfer operator (both having the spectral radius as an eigenvalue). We prove that the transfer operator has the spectral gap property in the space of Hölder continuous observables. From this we derive that the unique equilibrium state satisfies a central limit theorem and that it has exponential decay of correlations. Moreover, we prove joint continuity and analyticity with respect to the potential. (Based on various joint works with S. Afonso, J. Alves, V. Ramos.)

Online Zoom meeting (Session will open some minutes before 14h00)
https://videoconf-colibri.zoom.us/j/93397146959?pwd=dExCazBGM3Fvek9NU3F2MVNzTGF2Zz09

Meeting ID: 933 9714 6959

Password: 754835

Date and Venue

Start Date
Venue
Online seminar

Speaker

Jaqueline Siqueira

Speaker's Institution

Universidade Federal do Rio de Janeiro

Area

Dynamical Systems