On circle rotations and the shrinking target properties

Jimmy Tseng*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

28 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 languageEnglish
Pages (from-to)1111-1122
Number of pages12
JournalDiscrete and Continuous Dynamical Systems (DCDS-A)
Volume20
Issue number4
DOIs
Publication statusPublished - Apr 2008

Keywords

  • Circle rotations
  • Continued fractions
  • Diophantine approximation
  • Logarithm laws
  • Recurrence

Fingerprint

Dive into the research topics of 'On circle rotations and the shrinking target properties'. Together they form a unique fingerprint.

Cite this