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Iterated function systems and dynamical systems
We study the relationship between measures invariant for a piecewise expanding transformation of a compact metric space endowed with a underlying measure and measures invariant for an iterated functi...

Unstable evolution of pointwise trajectory solutions to chaotic maps

Chaos 5, 619 (1995); doi:10.1063/1.166132

Issue Date: December 1995

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Ronald F. Fox
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430
Simple chaotic maps are used to illustrate the inherent instability of trajectory solutions to the Frobenius–Perron equation. This is demonstrated by the difference in the behavior of delta-function solutions and of extended densities. Extended densities evolve asymptotically and irreversibly into invariant measures on stationary attractors. Pointwise trajectories chaotically roam over these attractors forever. Periodic Gaussian distributions on the unit interval are used to provide insight. Viewing evolving densities as ensembles of unstable pointwise trajectories gives densities a stochastic interpretation. ©1995 American Institute of Physics.
History: Received 23 March 1995; accepted 4 August 1995
Permalink: http://link.aip.org/link/?CHAOEH/5/619/1
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KEYWORDS and PACS

Keywords
PACS
  • 05.45.+b
    Statistical physics and thermodynamics Theory and models of chaotic systems
  • YEAR: 1995

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
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