Home > Articles > Published articles > Semiconjugacy to a map of a constant slope |
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 |
Rights: | Tots els drets reservats. |
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 |
Postprint 14 p, 328.8 KB |