Equilibrium stability for non-uniformly hyperbolic systems

• Type: Article in International Scientific Journal
• Date: 2019

Authors

alves, jf (Author) FCUP; Ramos, V (Author) Other; Siqueira, J (Author) Other

Journal

Title: Ergodic Theory and Dynamical Systems

Vol. 39

Pages: 2619-2642

ISSN: 0143-3857

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 4 Citations

Other information

Authenticus ID: P-00Q-G98

DOI: 10.1017/etds.2017.138

Abstract (EN): We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the topological pressure is continuous as a function of the dynamics and the potential. We also prove the existence of finitely many ergodic equilibrium states for non-uniformly hyperbolic skew products and hyperbolic Holder continuous potentials. Finally, we show that these equilibrium states vary continuously in the weak* topology within such systems.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 24