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

References in corpus (5)

• Pesin Entropy Formula for C1 Diffeomorphisms with Dominated Splitting
• SRB-like measures for C0 dynamics
• Ergodic theory of generic continuous maps
• Equilibrium States and SRB-like measures of C1 Expanding Maps of the Circle
• Weak Pseudo-Physical Measures and Pesin's Entropy Formula for Anosov C1 diffeomorphisms

Cited by in corpus (2)

• Typical properties of interval maps preserving the Lebesgue measure
• Topological and metric emergence of continuous maps