Constant slope, entropy and horseshoes for a map on a tame graph

Date(s) : 04/06/2019
11 h 00 min - 12 h 00 min

We study continuous countably (strictly) monotone maps defined on a tame graph, i.e., a special Peano continuum for which the set containing branchpoints and endpoints has countable closure. In our investigation we confine ourselves to the countable Markov case. We show a necessary and sufficient condition under which a locally eventually onto, countably Markov map {f} of a tame graph {G} is conjugate to a map {g} of constant slope. In particular, we show that in the case of a Markov map {f} that corresponds to a recurrent transition matrix, the condition is satisfied for constant slope {e}{h}({f}), where {h}({f}) is the topological entropy of {f} . Moreover, we show that in our class the topological entropy {h}({f}) is achievable through horseshoes of the map {f}.

Joint work with Adam Bartoš, Pavel Pyrih, Samuel Roth and Benjamin Vejnar.


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