Orbits closeness for slowly mixing dynamical systems

Jerome Rousseau, Mike Todd*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a dynamical system, we prove that the shortest distance between two n-orbits scales like n to a power even when the system has slow mixing properties, thus building and improving on results of Barros, Liao and the first author [On the shortest distance between orbits and the longest common substring problem. Adv. Math. 344 (2019), 311–339]. We also extend these results to flows. Finally, we give an example for which the shortest distance between two orbits has no scaling limit.
Original languageEnglish
Number of pages17
JournalErgodic Theory and Dynamical Systems
Early online date24 Jul 2023
Publication statusE-pub ahead of print - 24 Jul 2023


  • Shortest distance
  • Longest common substring
  • Correlation dimension
  • Inducing schemes


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