Estimating generating partitions of chaotic systems by unstable periodic orbits

Ruslan L. Davidchack, Ying-Cheng Lai, Erik M. Bollt, Mukeshwar Dhamala

Research output: Contribution to journalArticle

68 Citations (Scopus)

Abstract

An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.

Original languageEnglish
Pages (from-to)1353-1356
Number of pages4
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume61
Issue number2
DOIs
Publication statusPublished - 1 Feb 2000

Keywords

  • symbolic dynamics
  • strange attractor
  • ring cavity
  • henon map

Cite this

Estimating generating partitions of chaotic systems by unstable periodic orbits. / Davidchack, Ruslan L.; Lai, Ying-Cheng; Bollt, Erik M. ; Dhamala, Mukeshwar.

In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 61, No. 2, 01.02.2000, p. 1353-1356.

Research output: Contribution to journalArticle

Davidchack, Ruslan L. ; Lai, Ying-Cheng ; Bollt, Erik M. ; Dhamala, Mukeshwar. / Estimating generating partitions of chaotic systems by unstable periodic orbits. In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 2000 ; Vol. 61, No. 2. pp. 1353-1356.
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