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Journal Articles Nonlinearity Year : 2019

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.
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Dates and versions

hal-01915783 , version 1 (08-11-2018)

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Eleonora Catsigeras, Serge Troubetzkoy. Invariant measures for typical continuous maps on manifolds. Nonlinearity, 2019, 10, pp.3981-4001. ⟨hal-01915783⟩
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