Strange Attractors: Estimating the Complexity of Chaotic Signals View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1988

AUTHORS

Remo Badii , Antonio Politi

ABSTRACT

The discovery of simple dissipative systems yielding highly complex dynamical behavior1 has lead to the problem of characterizing and quantifying what is now generally called deterministic chaos. The most appropriate indicators of chaos so far introduced can be divided into three distinct classes: fractal dimensions (FD), metric entropies (ME), and Lyapunov exponents (LE). The main property which makes them relevant in the description of attractors is their invariance under smooth changes of coordinates. On the other hand, ‘old’ indicators like power spectra and auto-correlation functions can be considered as obsolete, not allowing to distinguish between truly deterministic chaos and stochastic motion: in both cases the spectrum is broad-band and the correlations decay exponentially. However, recent results for one-dimensional maps suggest the existence of interesting relations: the asymptotic time decay of auto-correlation functions can be expressed, for piecewise linear maps, in terms of generalized Lyapunov exponents.2 More... »

PAGES

335-362

References to SciGraph publications

  • 1978-07. Quantitative universality for a class of nonlinear transformations in JOURNAL OF STATISTICAL PHYSICS
  • 1986. On the Fractal Dimension of Filtered Chaotic Signals in DIMENSIONS AND ENTROPIES IN CHAOTIC SYSTEMS
  • Book

    TITLE

    Instabilities and Chaos in Quantum Optics II

    ISBN

    978-1-4899-2550-3
    978-1-4899-2548-0

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-1-4899-2548-0_22

    DOI

    http://dx.doi.org/10.1007/978-1-4899-2548-0_22

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1010778322


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