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${}^{\ast }$ closure of the set of ergodic measurescoincides with the weak${}^{\ast }$ closure of the set of measures supported on periodic orbits and also coincides withthe set of pseudo-physical measures. Furthermore, we show that this set has empty interior in the set of invariant measures.

arXiv admin note: text overlap with arXiv:1705.10133