Closest distance between iterates of typical points

Boyuan Zhao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The shortest distance between the first n iterates of a typical point can be quantified with a log rule for some dynamical systems admitting Gibbs measures. We show this in two settings. For topologically mixing Markov shifts with at most countably infinite alphabet admitting a Gibbs measure with respect to a locally Hölder potential, we prove the asymptotic length of the longest common substring for a typical point converges and the limit depends on the Rényi entropy. For interval maps with a Gibbs-Markov structure, we prove a similar rule relating the correlation dimension of Gibbs measures with the shortest distance between two iterates in the orbit generated by a typical point.
Original languageEnglish
Number of pages28
JournalDiscrete and Continuous Dynamical Systems - Series A
VolumeEarly Access
Early online date11 Mar 2024
Publication statusE-pub ahead of print - 11 Mar 2024


  • Symbolic dynamics
  • Closest distance within orbits
  • Countable Markov subshifts
  • Gibbs-Markov maps
  • Renyi entropy
  • Correlation dimension


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