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arxiv: 1811.04805 · v1 · pith:E4LN4VR2new · submitted 2018-11-09 · 🧮 math.DS

Invariant measures for typical continuous maps on manifolds

Eleonora Catsigeras (IMERL) , Serge Troubetzkoy (I2M) This is my paper
classification 🧮 math.DS
keywords measuresinvarianttypicalclosuremanifoldsmapsweakboundary
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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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  1. Physical-like Measures Coincide with Invariant Measures Supported on Chain Recurrent Classes

    math.DS 2019-07 unverdicted novelty 6.0

    For C^0 generic continuous maps or homeomorphisms on compact Riemannian manifolds, physical-like measures coincide with invariant measures supported on chain recurrent classes.