Semiconjugacy to a map of a constant slope

Lluís Alseda, Michal Misiurewicz

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

It is well known that a continuous piecewise monotone interval map with positive topological entropy is semiconjugate to a map of a con-stant 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 contin-uous 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.
Original languageEnglish
Pages (from-to)3403-3413
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume20
Issue number10
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Interval Markov maps
  • Measure of maximal entropy
  • Piecewise monotonotone maps
  • Semiconjugacy to a map of constant slope
  • Topological entropy

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