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

Adam Abrams; Svetlana Katok; Ilie Ugarcovici

doi:10.1088/1361-6544/acc6b2

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

Adam Abrams, Svetlana Katok, Ilie Ugarcovici

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	2894-2908
Number of pages	15
Journal	Nonlinearity
Volume	36
Issue number	5
DOIs	https://doi.org/10.1088/1361-6544/acc6b2
State	Published - 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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On the topological entropy of (a, b)-continued fraction transformations

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All Science Journal Classification (ASJC) codes

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