Rotation number and one-parameter families of circle diffeomorphisms

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9 Citations (Scopus)

Abstract

We consider one-parameter families of circle diffeomorphisms, f1(x) = f(x) + t(t 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.

Original languageEnglish
Pages (from-to)359-363
Number of pages5
JournalErgodic Theory and Dynamical Systems
Volume12
Issue number2
DOIs
Publication statusPublished - Jan 1 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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