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Entropy and volume as measures of orbit complexity

  • A. Classical Nonlinear Dynamics and Chaos
  • Conference paper
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The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function

Part of the book series: Lecture Notes in Physics ((LNP,volume 278))

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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.

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References

  1. R. Bowen, Entropy for Group Endomorphisms and Homogeneous Spaces, Trans. Amer. Math. Soc. 153 (1971), 401–414, 181(1973), 509-510.

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  4. S. Newhouse, Entropy and Volume, to appear in Jour. Ergodic Theory and Dyn. Sys.

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  5. S. Newhouse, Continuity Properties of Entropy, preprint, Mathematics Department, University of North Carolina, Chapel Hill, NC 27514, USA.

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  6. 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.

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Author information

Authors and Affiliations

  1. Mathematics Department, University of North Carolina, 27514, Chapel Hill, North Carolina

    Sheldon E. Newhouse

Authors
  1. Sheldon E. Newhouse
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Editor information

Y. S. Kim W. W. Zachary

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© 1987 Springer-Verlag

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Newhouse, S.E. (1987). Entropy and volume as measures of orbit complexity. In: Kim, Y.S., Zachary, W.W. (eds) The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function. Lecture Notes in Physics, vol 278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17894-5_304

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  • DOI: https://doi.org/10.1007/3-540-17894-5_304

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17894-1

  • Online ISBN: 978-3-540-47901-7

  • eBook Packages: Springer Book Archive

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