Unstable dimension variability and complexity in chaotic systems

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


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 (US)
Pages (from-to)R3807-R3810
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number4
StatePublished - 1999
Externally publishedYes

ASJC Scopus subject areas

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


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