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No division and the set of periods for tree maps

Published online by Cambridge University Press:  19 September 2008

Lluís Alsedà  and
Xiangdong Ye
Lluís Alsedà
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193-Bellaterra, Barcelona, Spain
Xiangdong Ye
Affiliation:
Section of Mathematics, International Center for Theoretic Physics, PO Box 586, 34100 Trieste, Italy
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Abstract

We extend the notion of no division for star maps to tree maps and prove that the set of periods of a tree map is cofinite if there exists some periodic orbit of the given map with period larger than one having no division. Using this result we obtain somesimple proofs of known results about the set of periods of a tree map. Also we show that this set is a union of initial segments of a finite number of linear orderings which depend only on the given tree minus a finite subset of ℕ.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 2 , April 1995 , pp. 221 - 237
Copyright
Copyright © Cambridge University Press 1995

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References

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