Output Functions and Fractal Dimensions in Dynamical Systems,

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the output function evaluation (OFE) method. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with D < 0.5, where D is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.

Original languageEnglish
Pages (from-to)2778-2781
Number of pages3
JournalPhysical Review Letters
Volume86
Publication statusPublished - 2001

Keywords

  • CHAOTIC SCATTERING
  • BASIN BOUNDARIES
  • METAMORPHOSES
  • BIFURCATION
  • TRANSIENTS
  • ESCAPE
  • ORBITS

Cite this

Output Functions and Fractal Dimensions in Dynamical Systems, / Moura, Alessandro Paula Servio; Grebogi, Celso.

In: Physical Review Letters, Vol. 86, 2001, p. 2778-2781.

Research output: Contribution to journalArticle

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AB - We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the output function evaluation (OFE) method. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with D < 0.5, where D is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.

KW - CHAOTIC SCATTERING

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KW - METAMORPHOSES

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KW - TRANSIENTS

KW - ESCAPE

KW - ORBITS

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