A Note on a Theorem of Parry

Details A Note on a Theorem of Parry A Note on a Theorem of Parry

2010-08-04

arxiv.org/abs/1008.0818v1

Mathematics

Dynamical Systems

15 pages

Scientific paper

A well-known result of Bill Parry shows that a topologically transitive continuous piecewise monotone mapping with positive topological entropy is conjugate to a uniformly piecewise linear mapping with slope determined by the entropy. In this note we generalise Parry's result somewhat to what we call the class of essentially transitive mappings. This generalisation is of some interest in as much as for mappings with one turning point the converse also holds, i.e., a uniformly piecewise linear mapping with one turning point and with slope greater than 1 is essentially transitive.

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