Unstable dimension variability and complexity in chaotic systems

Y C Lai, Ying-Cheng Lai

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We examine the interplay between complexity and unstable periodic orbits in high-dimensional chaotic systems. Argument and numerical evidence are presented suggesting that complexity can arise when the system is severely nonhyperbolic in the sense that periodic orbits with a distinct number of unstable directions coexist and are densely mixed. A quantitative measure is introduced to characterize this unstable dimension variability.

Original languageEnglish
Pages (from-to)R3807-R3810
Number of pages4
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number4
Publication statusPublished - Apr 1999

Keywords

  • PERIODIC-ORBITS
  • DYNAMICAL-SYSTEMS
  • RING CAVITY
  • ATTRACTORS
  • BASINS

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