Browsing by Subject "topological entropy"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Entropy locking
    (2018) Cosper, David; Misiurewicz, Michał; Mathematical Sciences, School of Science
    We prove that in certain one-parameter families of piecewise continuous piecewise linear interval maps with two laps, topological entropy stays constant as the parameter varies. The proof is simple and applies to a large set of families.
  • Thumbnail Image
    Item
    Semiconjugacy to a map of a constant slope
    (AIMS, 2015-12) Alsedà, Lluís; Misiurewicz, Michał; Department of Mathematical Sciences, School of Science
    It is well known that a continuous piecewise monotone interval map with positive topological entropy is semiconjugate to a map of a constant slope and the same entropy, and if it is additionally transitive then this semiconjugacy is actually a conjugacy. We generalize this result to piecewise continuous piecewise monotone interval maps, and as a consequence, get it also for piecewise monotone graph maps. We show that assigning to a continuous transitive piecewise monotone map of positive entropy a map of constant slope conjugate to it defines an operator, and show that this operator is not continuous.
  • Thumbnail Image
    Item
    Topological entropy of Bunimovich stadium billiards
    (2020) Misiurewicz, Michal; Zhang, Hong-Kun; Mathematical Sciences, School of Science
    We estimate from below the topological entropy of the Bunimovich stadium billiards. We do it for long billiard tables, and find the limit of estimates as the length goes to infinity.