### 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 |
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Pages (from-to) | 359-363 |

Number of pages | 5 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 12 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1992 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

**Rotation number and one-parameter families of circle diffeomorphisms.** / Masato, Tsujii.

Research output: Contribution to journal › Article

*Ergodic Theory and Dynamical Systems*, vol. 12, no. 2, pp. 359-363. https://doi.org/10.1017/S0143385700006805

}

TY - JOUR

T1 - Rotation number and one-parameter families of circle diffeomorphisms

AU - Masato, Tsujii

PY - 1992/1/1

Y1 - 1992/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84971840226&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84971840226&partnerID=8YFLogxK

U2 - 10.1017/S0143385700006805

DO - 10.1017/S0143385700006805

M3 - Article

AN - SCOPUS:84971840226

VL - 12

SP - 359

EP - 363

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 2

ER -