On the topological entropy of (a, b)-continued fraction transformations

Adam Abrams, Svetlana Katok, Ilie Ugarcovici

Research output: Contribution to journalArticlepeer-review


We study the topological entropy of a two-parameter family of maps related to (a, b)-continued fraction algorithms and prove that it is constant on a square within the parameter space (two vertices of this square correspond to well-studied continued fraction algorithms). The proof uses conjugation to maps of constant slope. We also present experimental evidence that the topological entropy is flexible (i.e. takes any value in a range) on the whole parameter space.

Original languageEnglish (US)
Pages (from-to)2894-2908
Number of pages15
Issue number5
StatePublished - May 1 2023

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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