Large deviations in chaotic systems: Exact results and dynamical phase transition

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6 Scopus citations

Abstract

Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths N generated by chaotic maps. The distributions generally display an exponential decay with N, associated with large-deviation (rate) functions. We obtain the exact rate functions analytically for the doubling, tent, and logistic maps. For the latter two, the solution is given as a power series whose coefficients can be systematically calculated to any order. We also obtain the rate function for the cat map numerically, uncovering strong evidence for the existence of a remarkable singularity of it that we interpret as a second-order dynamical phase transition. Furthermore, we develop a numerical tool for efficiently simulating atypical realizations of sequences if the chaotic map is not invertible, and we apply it to the tent and logistic maps.

Original languageEnglish
Article numberL042202
JournalPhysical Review E
Volume106
Issue number4
DOIs
StatePublished - 1 Oct 2022

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

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