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Ergodic Theory of Chaotic Dynamical Systems

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From Topology to Computation: Proceedings of the Smalefest

Abstract

A dynamical system in this article consists of a map of a manifold to itself or a flow generated by an autonomous system of ordinary differential equations. For definiteness, we shall discuss the discrete-time case, although most things here have their continuous-time versions. We shall not attempt to define “chaos, ” except to mention two of its essential ingredients:

  1. 1.

    exponential divergence of nearby orbits

  2. 2.

    lack of predictability.

This is an expanded version of a lecture presented in Berkeley in August 1990, in a conference honoring Steve Smale on his 60th birthday. The author is partially supported by NSF.

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Authors
  1. L.-S. Young
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Morris W. Hirsch

  2. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Jerrold E. Marsden

  3. IBM Research, T.J. Watson Research Center, 10598-0218, Yorktown Heights, NY, USA

    Michael Shub

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© 1993 Springer-Verlag New York, Inc.

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Young, LS. (1993). Ergodic Theory of Chaotic Dynamical Systems. In: Hirsch, M.W., Marsden, J.E., Shub, M. (eds) From Topology to Computation: Proceedings of the Smalefest. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2740-3_21

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  • DOI: https://doi.org/10.1007/978-1-4612-2740-3_21

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7648-7

  • Online ISBN: 978-1-4612-2740-3

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