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International Journal of Mathematics and Mathematical Sciences - Volume 2005 2005, Issue 19, Pages 3025-3033

Departament d-Informàtica i Matemàtica Aplicada, Universitat de Girona, Lluís Santaló s-n, Girona 17071, Spain

Received 5 May 2005; Revised 22 September 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.





Author: Esther Barrabés and David Juher

Source: https://www.hindawi.com/



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