# Rotation number and one-parameter families of circle diffeomorphisms

Research output: Contribution to journalArticle

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 language English 359-363 5 Ergodic Theory and Dynamical Systems 12 2 https://doi.org/10.1017/S0143385700006805 Published - Jan 1 1992 Yes

### Fingerprint

Rotation number
Minimal Set
Diffeomorphisms
Circle
Decomposition
Subshift
Topological Invariants
Finite Type
Family
Decompose
Interval
Invariant
Theorem

### All Science Journal Classification (ASJC) codes

• Mathematics(all)
• Applied Mathematics

### Cite this

In: Ergodic Theory and Dynamical Systems, Vol. 12, No. 2, 01.01.1992, p. 359-363.

Research output: Contribution to journalArticle

title = "Rotation number and one-parameter families of circle diffeomorphisms",
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.",
author = "Tsujii Masato",
year = "1992",
month = "1",
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language = "English",
volume = "12",
pages = "359--363",
journal = "Ergodic Theory and Dynamical Systems",
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T1 - Rotation number and one-parameter families of circle diffeomorphisms

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AB - 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.

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JO - Ergodic Theory and Dynamical Systems

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