Advertisement

Symbolic Dynamical Resolution of Power Spectra

  • M. A. Sepúlveda
  • R. Badii
Part of the NATO ASI Series book series (NSSB, volume 208)

Abstract

Power spectra have been for a long time employed as a means for the characterization of experimental time signals. After the discovery of low-dimensional chaotic behaviour in physical systems the analysis of power spectra contributed to the detailed understanding of transitions to chaos by period-doubling and quasiperiodicity 1. However, their usefulness for the investigation of typical chaos has been questioned, since they are not invariant under smooth coordinate changes 1. Here we show that power spectra are characterized by the topological and the metric properties of symbolic orbits, together with the actual numerical values of the observable. The former two ingredients are dynamical invariants and affect the spectra much more deeply than the latter one, which is obviously non-invariant.

Keywords

Power Spectrum Periodic Orbit Invariant Measure Logic Tree Symbolic Sequence 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J.P. Eckmann and D. Ruelle, Rev.Mod.Phys. 57, 617 (1985).MathSciNetCrossRefGoogle Scholar
  2. [2]
    M.A. Sepúlveda, R. Badii and E. Pollak, to be published.Google Scholar
  3. [3]
    R. Badii, Unfolding Complexity in Nonlinear Dynamical Systems,this issue; Quantitative Characterization of Complexity and Predictability,submitted for publication.Google Scholar
  4. [4]
    M. Hénon, Comm.Math.Phys. 50, 69 (1976).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • M. A. Sepúlveda
    • 1
    • 2
  • R. Badii
    • 1
    • 2
  1. 1.Chemical Physics Dept.The Weizmann InstituteRehovotIsrael
  2. 2.Fakultät für PhysikUniversität KonstanzConstanceW.Germany

Personalised recommendations