Invariant measures for typical continuous maps on manifolds

Eleonora Catsigeras (IMERL); Serge Troubetzkoy (I2M)

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Invariant measures for typical continuous maps on manifolds

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arxiv 1811.04805 v1 pith:E4LN4VR2 submitted 2018-11-09 math.DS

Eleonora Catsigeras (IMERL) , Serge Troubetzkoy (I2M) This is my paper · ORCID

classification math.DS

keywords measuresinvarianttypicalclosuremanifoldsmapsweakboundary

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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 measurescoincides with the weak$^*$ 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.

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