Semiconjugacy to a map of a constant slope

2014/10/07 by Lluís Alsedà, Michał Misiurewicz, Alsedà, Lluís +1 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1410.1718

arxiv created 2014/10/07 · arxiv updated 2014/10/08

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.

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• The boundary of chaos for piecewise smooth maps and the boundary of positive Hausdorff dimension for survivor sets of open maps

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