Rotation sets for orbits of degree one circle maps

Lluís Alsedà; Francesc Mañosas; Moira Chas

doi:https://doi.org/10.1142/S0218127402004437

Rotation sets for orbits of degree one circle maps

Lluís Alsedà, Francesc Mañosas, Moira Chas

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

Let F be the lifting of a circle map of degree one. In [Bamón et al., 1984] a notion of F-rotation interval of a point x ∈ S1 was given. In this paper we define and study a new notion of a rotation set of a point which preserves more of the dynamical information contained in the sequences {Fn(y)}n=0∞ than the one preserved from [Bamón et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamón et al., 1984] in our settings.

Original language	English
Pages (from-to)	429-437
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	12
DOIs	https://doi.org/10.1142/S0218127402004437
Publication status	Published - 1 Jan 2002

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title = "Rotation sets for orbits of degree one circle maps",

abstract = "Let F be the lifting of a circle map of degree one. In [Bam{\'o}n et al., 1984] a notion of F-rotation interval of a point x ∈ S1 was given. In this paper we define and study a new notion of a rotation set of a point which preserves more of the dynamical information contained in the sequences {Fn(y)}n=0∞ than the one preserved from [Bam{\'o}n et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bam{\'o}n et al., 1984] in our settings.",

author = "Llu{\'i}s Alsed{\`a} and Francesc Ma{\~n}osas and Moira Chas",

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AU - Mañosas, Francesc

AU - Chas, Moira

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N2 - Let F be the lifting of a circle map of degree one. In [Bamón et al., 1984] a notion of F-rotation interval of a point x ∈ S1 was given. In this paper we define and study a new notion of a rotation set of a point which preserves more of the dynamical information contained in the sequences {Fn(y)}n=0∞ than the one preserved from [Bamón et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamón et al., 1984] in our settings.

AB - Let F be the lifting of a circle map of degree one. In [Bamón et al., 1984] a notion of F-rotation interval of a point x ∈ S1 was given. In this paper we define and study a new notion of a rotation set of a point which preserves more of the dynamical information contained in the sequences {Fn(y)}n=0∞ than the one preserved from [Bamón et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamón et al., 1984] in our settings.

U2 - https://doi.org/10.1142/S0218127402004437

DO - https://doi.org/10.1142/S0218127402004437

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VL - 12

SP - 429

EP - 437

ER -