The twisted baker map

Yoshitaka Saiki, Hiroki Takahasi, James A. Yorke

Research output: Contribution to journalArticlepeer-review

Abstract

As a model to provide a hands-on, elementary understanding of ‘vortex dynamics’, we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex conjugate eigenvalues and that without complex conjugate eigenvalues are simultaneously dense in the phase space. We also show that these two sets equidistribute with respect to the normalised Lebesgue measure, in spite of a non-uniformity in their Lyapunov exponents.

Original languageEnglish
Pages (from-to)1776-1788
Number of pages13
JournalNonlinearity
Volume36
Issue number3
DOIs
Publication statusPublished - 2023 Mar 1

Keywords

  • baker map
  • equidistribution
  • mixing
  • periodic point
  • piecewise linear map

ASJC Scopus subject areas

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

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