Semiconjugacy to a map of a constant slope
Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Misiurewicz, Michal (IUPUI (Indianapolis). Department of Mathematical Sciences)

Date:	2015
Abstract:	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.
Grants:	Ministerio de Educación y Ciencia MTM2008-01486 Ministerio de Educación y Ciencia MTM2011-26995-C02-01
Note:	Preprint
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Interval Markov maps ; Measure of maximal entropy ; Piecewise monotonotone maps ; Semiconjugacy to a map of constant slope ; Topological entropy
Published in:	Discrete and continuous dynamical systems. Series B, Vol. 20 Núm. 10 (2015) , p. 2043-2413, ISSN 1553-524X

DOI: 10.3934/dcdsb.2015.20.3403

Postprint 14 p, 328.8 KB

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