Semiconjugacy to a map of a constant slope | Zendy

Lluı́s Alsedà | Zendy; Michał Misiurewicz | Zendy

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Semiconjugacy to a map of a constant slope

Author(s) -

Lluı́s Alsedà,

Michał Misiurewicz

Publication year - 2015

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2015.20.3403

Subject(s) - topological entropy , piecewise , mathematics , continuous map , monotone polygon , transitive relation , entropy (arrow of time) , graph , constant (computer programming) , discrete mathematics , pure mathematics , combinatorics , mathematical analysis , geometry , computer science , physics , quantum mechanics , programming language

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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