2019/09/16 by Tamara Kucherenko, D. J. D. Thompson, Kucherenko, Tamara +1
Mathematics · #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1909.07317
Given a compact topological dynamical system (X, f) with positive entropy and\nupper semi-continuous entropy map, and any closed invariant subset Y \⊂\nX with positive entropy, we show that there exists a continuous roof function\nsuch that the set of measures of maximal entropy for the suspension semi-flow\nover (X,f) consists precisely of the lifts of measures which maximize entropy\non Y. This result has a number of implications for the possible size of the set\nof measures of maximal entropy for topological suspension flows. In particular,\nfor a suspension flow on the full shift on a finite alphabet, the set of\nergodic measures of maximal entropy may be countable, uncountable, or have any\nfinite cardinality.\n