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The minimum tree for a given zero-entropy period

We answer the following question: given any n∈ℕ, which is the minimum number of endpoints en of a tree admitting a zero-entropy map f with a periodic orbit of period n? We prove that en=s1s2…sk−∑i=2ksisi+1…sk, where n=s1s2…sk is the decomposition of n into a product of primes such that si≤si+1 for 1≤ie, then the topological entropy of f is positive

Hindawi Publishing Corporation

Author: Barrabés Vera, Esther
Juher, David
Abstract: We answer the following question: given any n∈ℕ, which is the minimum number of endpoints en of a tree admitting a zero-entropy map f with a periodic orbit of period n? We prove that en=s1s2…sk−∑i=2ksisi+1…sk, where n=s1s2…sk is the decomposition of n into a product of primes such that si≤si+1 for 1≤ie, then the topological entropy of f is positive
Document access: http://hdl.handle.net/2072/227224
Language: eng
Publisher: Hindawi Publishing Corporation
Rights: Attribution 3.0 Spain
Rights URI: http://creativecommons.org/licenses/by/3.0/es/
Subject: Ã’rbites
Orbits
Entropia topològica
Topological entropy
Title: The minimum tree for a given zero-entropy period
Type: info:eu-repo/semantics/article
Repository: Recercat

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