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Entropy and volume as measures of orbit complexity

  • Sheldon E. Newhouse
A. Classical Nonlinear Dynamics and Chaos
Part of the Lecture Notes in Physics book series (LNP, volume 278)

Abstract

Topological entropy and volume growth of smooth disks are considered as measures of the orbit complexity of a smooth dynamical system. In many cases, topological entropy can be estimated via volume growth. This gives methods of estimating dynamical invariants of transient and attracting sets and may apply to time series.

Keywords

Strange Attractor Volume Growth Topological Entropy Riemann Sphere Dynamical Invariant 
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

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    R. Bowen, Entropy for Group Endomorphisms and Homogeneous Spaces, Trans. Amer. Math. Soc. 153 (1971), 401–414, 181(1973), 509-510.MathSciNetCrossRefMATHGoogle Scholar
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    M. Ljubich, Entropy properties of rational endomorphisms of the Riemann Sphere, Jour. Ergodic Theory and Dyn. Sys. 3 (1983), 351–387.MathSciNetGoogle Scholar
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    S. Newhouse, Entropy and Volume, to appear in Jour. Ergodic Theory and Dyn. Sys.Google Scholar
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    S. Newhouse, Continuity Properties of Entropy, preprint, Mathematics Department, University of North Carolina, Chapel Hill, NC 27514, USA.Google Scholar
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    Y. Yomdin, Volume Growth and Entropy, and Ck-resolution of Semi-algebraic Mappings—Addendum to the Volume Growth and Entropy, to appear in Israel J. of Math.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Sheldon E. Newhouse
    • 1
  1. 1.Mathematics DepartmentUniversity of North CarolinaChapel Hill

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