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D-function of a minimal set and an extension of Sharkovskii's theorem to minimal sets

Published online by Cambridge University Press:  19 September 2008

Xiangdong Ye
Xiangdong Ye
Affiliation:
Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720, USA
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Abstract

Let X be a compact Hausdorff space, f ∈ C0(X, X) and A ⊂ X a minimal set of f. We first introduce a new topological invariant, the D-function of a minimal set, by the investigation of the decomposition of the minimal set A under the action of fn, n ∈ N. Then important properties about the invariant and the existence of minimal set with a given D-function in some subshift of finite type are discussed. Finally Sharkovskii's theorem is generalized to minimal sets of continuous mappings from the interval into itself.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 2 , June 1992 , pp. 365 - 376
Copyright
Copyright © Cambridge University Press 1992

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