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arXiv · 1705.10133

Pseudo-physical measures for typical continuous maps of the interval

Eleonora Catsigeras·Serge Troubetzkoy
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Abstract

We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is in the closure of the ergodic measures, as well as in the closure of the atomic measures. We show that the set of pseudo-physical measures is meager in the space of all invariant measures. Finally, we study the entropy function. We construct pseudo-physical measures with infinite entropy. We also prove that, for each m $\ge$ 1, there exists infinitely many pseudo-physical measures with entropy log m, and deduce that the entropy function is neither upper semi-continuous nor lower semi-continuous.

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Eleonora Catsigeras, Serge Troubetzkoy. 2017-05-29. Pseudo-physical measures for typical continuous maps of the interval. https://arxiv.org/abs/1705.10133

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