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Semiconjugacy to a map of a constant slope
Alsedà, Lluís
Misiurewicz, Michal

Data: 2015
Resum: 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.
Nota: Preprint
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: interval Markov maps ; measure of maximal entropy ; Piecewise monotonotone maps ; semiconjugacy to a map of constant slope ; topological entropy
Publicat a: Discrete and Continuous Dynamical Systems. Series B, Vol. 20 Núm. 10 (2015) , p. 2043-2413

DOI: 10.3934/dcdsb.2015.20.3403

14 p, 328.8 KB

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