Introduction to Transient Chaos

Ying Cheng Lai, T. Tél

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In numerical or experimental investigations one never has infinitely long time intervals at one’s disposal. In fact, what is needed for the observation of chaos is a well-defined separation of time scales. Let t 0 denote the internal characteristic time of the system. In continuous-time problems, t 0 can be the average turnover time of trajectories on a Poincaré map in the phase space. In a driven system, it is the driving period. In discrete-time dynamics, t 0 can be the time step itself.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages3-35
Number of pages33
DOIs
Publication statusPublished - Jan 1 2011

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume173
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Chaotic Attractor
  • Homoclinic Orbit
  • Lyapunov Exponent
  • Stable Manifold
  • Unstable Manifold

ASJC Scopus subject areas

  • Applied Mathematics

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  • Cite this

    Lai, Y. C., & Tél, T. (2011). Introduction to Transient Chaos. In Applied Mathematical Sciences (Switzerland) (pp. 3-35). (Applied Mathematical Sciences (Switzerland); Vol. 173). Springer. https://doi.org/10.1007/978-1-4419-6987-3_1