Contribution to the ergodic theory of robustly transitive maps
2014
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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