Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors View Full Text


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Article Info

DATE

1988-04

AUTHORS

P. Grassberger, R. Badii, A. Politi

ABSTRACT

The analysis of dynamical systems in terms of spectra of singularities is extended to higher dimensions and to nonhyperbolic systems. Prominent roles in our approach are played by the generalized partial dimensions of the invariant measure and by the distribution of effective Liapunov exponents. For hyperbolic attractors, the latter determines the metric entropies and provides one constraint on the partial dimensions. For nonhyperbolic attractors, there are important modifications. We discuss them for the examples of the logistic and Hénon map. We show, in particular, that the generalized dimensions have singularities with noncontinuous derivative, similar to first-order phase transitions in statistical mechanics. More... »

PAGES

135-178

References to SciGraph publications

  • 1980. Lectures on Dynamical Systems in DYNAMICAL SYSTEMS
  • 1984-06. Fully developed chaotic 1−d maps in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • 1984-09. Is the dimension of chaotic attractors invariant under coordinate changes? in JOURNAL OF STATISTICAL PHYSICS
  • 1981-09. Absolutely continuous invariant measures for one-parameter families of one-dimensional maps in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1976-02. A two-dimensional mapping with a strange attractor in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/bf01015324

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    http://dx.doi.org/10.1007/bf01015324

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