Contribution to the ergodic theory of robustly transitive maps

Cristina Lizana; Vilton Pinheiro; Paulo Varandas

doi:10.3934/dcds.2015.35.353

Article Contents

2015, Volume 35, Issue 1: 353-365. Doi: 10.3934/dcds.2015.35.353

This issue Previous Article A note on partially hyperbolic attractors: Entropy conjecture and SRB measures Next Article Symplectic groupoids and discrete constrained Lagrangian mechanics

Contribution to the ergodic theory of robustly transitive maps

1.
Departamento de Matemática, Facultad de Ciencias, La Hechicera, Universidad de los Andes Mérida, 5101
2.
Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador

Received: December 31, 2013

Revised: March 31, 2014

Published: December 2014

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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.

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Mathematics Subject Classification: Primary: 37A25, 37C40; Secondary: 37D25.

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