Statistical description of chaotic attractors: The dimension function View Full Text


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Article Info

DATE

1985-09

AUTHORS

Remo Radii, Antonio Politi

ABSTRACT

A method for the investigation of fractal attractors is developed, based on statistical properties of the distributionP(δ, n) of nearest-neighbor distancesδ between points on the attractor. A continuous infinity of dimensions, called dimension function, is defined through the moments ofP(δ, n). In particular, for the case of self-similar sets, we prove that the dimension function DF yields, in suitable points, capacity, information dimension, and all other Renyi dimensions. An algorithm to compute DF is derived and applied to several attractors. As a consequence, an estimate of nonuniformity in dynamical systems can be performed, either by direct calculation of the uniformity factor, or by comparison among various dimensions. Finally, an analytical study of the distributionP(δ, n) is carried out in some simple, meaningful examples. More... »

PAGES

725-750

References to SciGraph publications

  • 1918-03. Dimension und äußeres Maß in MATHEMATISCHE ANNALEN
  • 1973-07. A statistical measure for the repulsion of energy levels in LETTERE AL NUOVO CIMENTO (1971-1985)
  • 1976-02. A two-dimensional mapping with a strange attractor in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01009897

    DOI

    http://dx.doi.org/10.1007/bf01009897

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1030567916


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