2017/05/29 by Eleonora Catsigeras, Catsigeras, Eleonora, Serge Troubetzkoy +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1705.10133
openalex publication_date 2017/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≥ 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.