Strange attractors with one direction of instability

Qiu-Dong Wang, Lai Sang Young

Research output: Contribution to journalArticle

114 Citations (Scopus)

Abstract

We give simple conditions that guarantee, for strongly dissipative maps, the existence of strange attractors with a single direction of instability and certain controlled behaviors. Only the d = 2 case is treated in this paper, although our approach is by no means limited to two phase-dimensions. We develop a dynamical picture for the attractors in this class, proving they have many of the statistical properties associated with chaos: positive Lyapunov exponents, existence of SRB measures, and exponential decay of correlations. Other results include the geometry of fractal critical sets, nonuniform hyperbolic behavior, symbolic coding of orbits, and formulas for topological entropy.

Original languageEnglish (US)
Pages (from-to)1-97
Number of pages97
JournalCommunications in Mathematical Physics
Volume218
Issue number1
DOIs
StatePublished - Apr 2001

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strange attractors
Strange attractor
Space Shuttle Boosters
SRB Measure
Critical Set
Fractal Set
Decay of Correlations
Topological Entropy
Exponential Decay
Lyapunov Exponent
Statistical property
chaos
Attractor
fractals
Chaos
coding
Coding
Orbit
exponents
entropy

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Strange attractors with one direction of instability. / Wang, Qiu-Dong; Young, Lai Sang.

In: Communications in Mathematical Physics, Vol. 218, No. 1, 04.2001, p. 1-97.

Research output: Contribution to journalArticle

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