Local rates of poincaré recurrence for rotations and weak mixing

J. R. Chazottes; F. Durand

Local rates of poincaré recurrence for rotations and weak mixing

J. R. Chazottes
, F. Durand

Université de Picardie Jules Verne

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

Abstract

We study the lower and upper local rates of Poincaré recurrence of rotations on the circle by means of symbolic dynamics. As a consequence, we show that if the lower rate of Poincaré recurrence of an ergodic dynamical system (X, ℱ, μ, T) is greater or equal to 1 μ-almost everywhere, then it is weakly mixing.

Original language	English
Pages (from-to)	175-183
Number of pages	9
Journal	Discrete and Continuous Dynamical Systems
Volume	12
Issue number	1
Publication status	Published - 1 Jan 2005

Keywords

Linearly recurrent subshift
Poincaré
Recurrence
Rotation
Sturmian subshift
Weak mixing

Cite this

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title = "Local rates of poincar{\'e} recurrence for rotations and weak mixing",

abstract = "We study the lower and upper local rates of Poincar{\'e} recurrence of rotations on the circle by means of symbolic dynamics. As a consequence, we show that if the lower rate of Poincar{\'e} recurrence of an ergodic dynamical system (X, ℱ, μ, T) is greater or equal to 1 μ-almost everywhere, then it is weakly mixing.",

keywords = "Linearly recurrent subshift, Poincar{\'e}, Recurrence, Rotation, Sturmian subshift, Weak mixing",

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year = "2005",

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T1 - Local rates of poincaré recurrence for rotations and weak mixing

AU - Chazottes, J. R.

AU - Durand, F.

PY - 2005/1/1

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N2 - We study the lower and upper local rates of Poincaré recurrence of rotations on the circle by means of symbolic dynamics. As a consequence, we show that if the lower rate of Poincaré recurrence of an ergodic dynamical system (X, ℱ, μ, T) is greater or equal to 1 μ-almost everywhere, then it is weakly mixing.

AB - We study the lower and upper local rates of Poincaré recurrence of rotations on the circle by means of symbolic dynamics. As a consequence, we show that if the lower rate of Poincaré recurrence of an ergodic dynamical system (X, ℱ, μ, T) is greater or equal to 1 μ-almost everywhere, then it is weakly mixing.

KW - Linearly recurrent subshift

KW - Poincaré

KW - Recurrence

KW - Rotation

KW - Sturmian subshift

KW - Weak mixing

M3 - Article

AN - SCOPUS:15744400112

SN - 1078-0947

VL - 12

SP - 175

EP - 183

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 1

ER -

Local rates of poincaré recurrence for rotations and weak mixing

Abstract

Keywords

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