On circle rotations and the shrinking target properties

Jimmy Tseng

doi:10.3934/dcds.2008.20.1111

On circle rotations and the shrinking target properties

Jimmy Tseng^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

38 Citations (Scopus)

Abstract

We generalize the monotone shrinking target property (MSTP) to the s-exponent monotone shrinking target property (sMSTP) and give a necessary and sufficient condition for a circle rotation to have sMSTP. Using another variant of MSTP, we obtain a new, very short, proof of a known result, which concerns the behavior of irrational rotations and implies a logarithm law similar to D. Sullivan's logarithm law for geodesics.

Original language	English
Pages (from-to)	1111-1122
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems (DCDS-A)
Volume	20
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2008.20.1111
Publication status	Published - Apr 2008

Keywords

Circle rotations
Continued fractions
Diophantine approximation
Logarithm laws
Recurrence

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AB - We generalize the monotone shrinking target property (MSTP) to the s-exponent monotone shrinking target property (sMSTP) and give a necessary and sufficient condition for a circle rotation to have sMSTP. Using another variant of MSTP, we obtain a new, very short, proof of a known result, which concerns the behavior of irrational rotations and implies a logarithm law similar to D. Sullivan's logarithm law for geodesics.

KW - Circle rotations

KW - Continued fractions

KW - Diophantine approximation

KW - Logarithm laws

KW - Recurrence

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DO - 10.3934/dcds.2008.20.1111

M3 - Article (Academic Journal)

AN - SCOPUS:44849096878

SN - 1078-0947

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JO - Discrete and Continuous Dynamical Systems (DCDS-A)

JF - Discrete and Continuous Dynamical Systems (DCDS-A)

IS - 4

ER -

On circle rotations and the shrinking target properties

Abstract

Keywords

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