Title:
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Sets of periods for piecewise monotone tree maps
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Author:
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Alseda Soler, Lluís; Juher, D.; Mumbrú i Rodriguez, Pere
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
Abstract:
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We study the set of periods of tree maps f : T −→ T which are monotone between any
two consecutive points of a fixed periodic orbit P. This set is characterized in terms of some
integers which depend only on the combinatorics of f|P and the topological structure of T. In
particular, a type p ≥ 1 of P is defined as a generalization of the notion introduced by Baldwin
in his characterization of the set of periods of star maps. It follows that there exists a divisor
k of the period of P such that if the set of periods of f is not finite then it contains either all
the multiples of kp or an initial segment of the kp≥ Baldwin’s ordering, except for a finite set
which is explicitly bounded. Conversely, examples are given where f has precisely these sets of
periods. |
Subject(s):
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-Differentiable dynamical systems -tree maps -Sistemes dinàmics diferenciables -Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems |
Rights:
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Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
Document type:
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Article |
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