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Tree maps with non divisible periodic orbits
Published online by Cambridge University Press: 17 April 2009
Abstract
Let End (T) be the number of ends of a tree T and f: T → T be continuous. We show that f has a non divisible periodic orbit if and only if there are some x ∈ T and n > 1 with (n, m) = 1 for each 2 ≤ m ≤ End(T) such that x ∈ (f(x), fn(x)). Consequently the property of a tree map with a non divisible periodic orbit is preserved under small perturbation.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 467 - 471
- Copyright
- Copyright © Australian Mathematical Society 1997
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