The minimum tree for a given zero-entropy period

Esther Barrabés and David Juher

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-9

Abstract:

We answer the following question: given any n ∈ ℕ , which is the minimum number of endpoints e n of a tree admitting a zero-entropy map f with a periodic orbit of period n ? We prove that e n = s 1 s 2 … s k − ∑ i = 2 k s i s i + 1 … s k , where n = s 1 s 2 … s k is the decomposition of n into a product of primes such that s i ≤ s i + 1 for 1 ≤ i < k . As a corollary, we get a criterion to decide whether a map f defined on a tree with e endpoints has positive entropy: if f has a periodic orbit of period m with e m > e , then the topological entropy of f is positive.

Date: 2005
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2005/204938.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2005/204938.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:204938

DOI: 10.1155/IJMMS.2005.3025

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().