On circle rotations and the shrinking target properties

Jimmy Tseng*

*Corresponding author for this work

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

32 Citations (Scopus)


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)
Issue number4
Publication statusPublished - Apr 2008


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


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