Introduction to Transient Chaos

Ying-Cheng Lai, Tamás 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 (US)
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages3-35
Number of pages33
DOIs
StatePublished - Jan 1 2011

Publication series

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

Fingerprint

Chaos theory
Chaos
Trajectories
Time-average
Numerical Investigation
Experimental Investigation
Well-defined
Continuous Time
Phase Space
Discrete-time
Time Scales
Trajectory
Denote
Internal
Interval
Observation

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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

Introduction to Transient Chaos. / Lai, Ying-Cheng; Tél, Tamás.

Applied Mathematical Sciences (Switzerland). Springer, 2011. p. 3-35 (Applied Mathematical Sciences (Switzerland); Vol. 173).

Research output: Chapter in Book/Report/Conference proceedingChapter

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