Invariant measures for typical continuous maps on manifolds
Abstract
We study the invariant measures of typical $C^0$ maps on compact connected manifolds with or without boundary, and also of typical homeomorphisms. We prove that the weak$^*$ closure of the set of ergodic measures
coincides with the weak$^*$ closure of the set of measures supported on periodic orbits and also coincides with
the set of pseudo-physical measures. Furthermore, we show that this set has empty interior in the set of invariant measures.
Domains
Dynamical Systems [math.DS]
Origin : Files produced by the author(s)
Loading...