Presentation functions, fixed points, and a theory of scaling function dynamics View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1988-08

AUTHORS

Mitchell J. Feigenbaum

ABSTRACT

Presentation functions provide the time-ordered points of the forward dynamics of a system as successive inverse images. They generally determine objects constructed on trees, regular or otherwise, and immediately determine a functional form of the transfer matrix of these systems. Presentation functions for regular binary trees determine the associated forward dynamics to be that of a period doubling fixed point. They are generally parametrized by the trajectory scaling function of the dynamics in a natural way. The requirement that the forward dynamics be smooth with a critical point determines a complete set of equations whose solution is the scaling function. These equations are compatible with a dynamics in the space of scalings which is conjectured, with numerical and intuitive support, to possess its solution as a unique, globally attracting fixed point. It is argued that such dynamics is to be sought as a program for the solution of chaotic dynamics. In the course of the exposition new information pertaining to universal mode locking is presented. More... »

PAGES

527-569

References to SciGraph publications

  • 1987-03. Some characterizations of strange sets in JOURNAL OF STATISTICAL PHYSICS
  • 1980-02. The transition to aperiodic behavior in turbulent systems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Journal

    TITLE

    Journal of Statistical Physics

    ISSUE

    3-4

    VOLUME

    52

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01019716

    DOI

    http://dx.doi.org/10.1007/bf01019716

    DIMENSIONS

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