Topological Frequencies in Dynamical Systems

  • R. Gilmore
  • G. Mindlin
  • H. G. Solari
Part of the NATO ASI Series book series (NSSB, volume 208)

Abstract

In this work the presence of a seemingly anomalous peak at a non 2n frequency in the power spectrum of the period doubling attractor at the onset of chaos is discussed. Using tools from the theory of knots we study the behaviour of the topological invariant responsible for that effect in a wide class of systems.

Keywords

Periodic Solution Period Doubling Topological Invariant Chaotic Solution Anomalous Peak 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Gonzalez D., Magnasco M., Mindlin G., Romanelli L., Larrondo H: A universal departure from the classical period doubling spectrum. Physica D (in press).Google Scholar
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    Birman J.S., Williams R.F: Knotted periodic orbits in dynamical systems-I:Lorenz’s equations. Topology Vol.22 N1, 47, 1983.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Holmes P.: Knotted periodic orbits in suspensions of annulus maps. Proc.R Soc.Lond. A 441, 351, 1987.Google Scholar
  4. 4.
    Solari H.G, Gilmore R.: Relative rotation rates for driven dynamical systems. Physical Review A. Vol 37. N8, 3096, 1988.MathSciNetCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • R. Gilmore
    • 1
  • G. Mindlin
    • 1
  • H. G. Solari
    • 1
  1. 1.Department of Physics and Atmospheric SciencesDrexel UniversityPhiladelphiaUSA

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