Estimating generating partitions of chaotic systems by unstable periodic orbits

Citation
Rl. Davidchack et al., Estimating generating partitions of chaotic systems by unstable periodic orbits, PHYS REV E, 61(2), 2000, pp. 1353-1356
Citations number
25
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
61
Issue
2
Year of publication
2000
Pages
1353 - 1356
Database
ISI
SICI code
1063-651X(200002)61:2<1353:EGPOCS>2.0.ZU;2-N
Abstract
An outstanding problem in chaotic dynamics is to specify generating partiti ons for symbolic dynamics in dimensions larger than 1. It has been known th at 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 de fined with respect to periodic orbits. Our algorithm allows us to obtain th e approximate location of the generating partition for the Ikeda-Hammel-Jon es-Moloney map.