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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Contribution to the ergodic theory of robustly transitive maps

Pages: 353 - 365, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.353

 
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Cristina Lizana - Departamento de Matemática, Facultad de Ciencias, La Hechicera, Universidad de los Andes Mérida, 5101, Venezuela (email)
Vilton Pinheiro - Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil (email)
Paulo Varandas - Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil (email)

Abstract: In this article we intend to contribute in the understanding of the ergodic properties of the set of robustly transitive local diffeomorphisms on a compact manifold without boundary. We prove that $C^1$ generic robustly transitive local diffeomorphisms have a residual subset of points with dense pre-orbits. Moreover, $C^1$ generically in the space of local diffeomorphisms with no splitting and all points with dense pre-orbits, there are uncountably many ergodic expanding invariant measures with full support and exhibiting exponential decay of correlations. In particular, these results hold for an important class of robustly transitive maps.

Keywords:  Robust transitivity, endomorphisms, expanding measures, ergodic measures, invariant measures, decay of correlations.
Mathematics Subject Classification:  Primary: 37A25, 37C40; Secondary: 37D25.

Received: January 2014;      Revised: April 2014;      Available Online: August 2014.

 References