Measuring the Strangeness of Strange Attractors View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2004

AUTHORS

Peter Grassberger , Itamar Procaccia

ABSTRACT

We study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise. The exponent v is closely related to the fractal dimension and the information dimension, but its computation is considerably easier. Its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed. Algorithms for extracting v from the time series of a single variable are proposed. The relations between the various measures of strange attractors and between them and the Lyapunov exponents are discussed. It is shown that the conjecture of Kaplan and Yorke for the dimension gives an upper bound for v. Various examples of finite and infinite dimensional systems are treated, both numerically and analytically. More... »

PAGES

170-189

References to SciGraph publications

  • 1979-12. The universal metric properties of nonlinear transformations in JOURNAL OF STATISTICAL PHYSICS
  • 1981-09. On the Hausdorff dimension of fractal attractors in JOURNAL OF STATISTICAL PHYSICS
  • 1982-07. Noise in chaotic systems in NATURE
  • 1979. Chaotic behavior of multidimensional difference equations in FUNCTIONAL DIFFERENTIAL EQUATIONS AND APPROXIMATION OF FIXED POINTS
  • 1971-09. On the nature of turbulence in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1976-06. Simple mathematical models with very complicated dynamics in NATURE
  • Book

    TITLE

    The Theory of Chaotic Attractors

    ISBN

    978-1-4419-2330-1
    978-0-387-21830-4

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-0-387-21830-4_12

    DOI

    http://dx.doi.org/10.1007/978-0-387-21830-4_12

    DIMENSIONS

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