Minimal dynamics for tree maps

Lluís Alsedà; David Juher; Pere Mumbrú

Minimal dynamics for tree maps

Lluís Alsedà, David Juher, Pere Mumbrú

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

We prove that, given a tree pattern P, the set of periods of a minimal representative f: T → T of P is contained in the set of periods of any other representative. This statement is an immediate corollary of the following stronger result: there is a period-preserving injection from the set of periodic points of f into that of any other representative of P. We prove this result by extending the main theorem of [6] to negative cycles.

Original language	English
Pages (from-to)	511-541
Journal	Discrete and Continuous Dynamical Systems
Volume	20
Issue number	3
Publication status	Published - 1 Mar 2008

Keywords

Minimal dynamics
Tree maps

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title = "Minimal dynamics for tree maps",

abstract = "We prove that, given a tree pattern P, the set of periods of a minimal representative f: T → T of P is contained in the set of periods of any other representative. This statement is an immediate corollary of the following stronger result: there is a period-preserving injection from the set of periodic points of f into that of any other representative of P. We prove this result by extending the main theorem of [6] to negative cycles.",

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T1 - Minimal dynamics for tree maps

AU - Alsedà, Lluís

AU - Juher, David

AU - Mumbrú, Pere

PY - 2008/3/1

Y1 - 2008/3/1

N2 - We prove that, given a tree pattern P, the set of periods of a minimal representative f: T → T of P is contained in the set of periods of any other representative. This statement is an immediate corollary of the following stronger result: there is a period-preserving injection from the set of periodic points of f into that of any other representative of P. We prove this result by extending the main theorem of [6] to negative cycles.

AB - We prove that, given a tree pattern P, the set of periods of a minimal representative f: T → T of P is contained in the set of periods of any other representative. This statement is an immediate corollary of the following stronger result: there is a period-preserving injection from the set of periodic points of f into that of any other representative of P. We prove this result by extending the main theorem of [6] to negative cycles.

KW - Minimal dynamics

KW - Tree maps

M3 - Article

VL - 20

SP - 511

EP - 541

IS - 3

ER -