Measures Invariant under Mappings of the Unit Interval

  • Pierre Collet
  • Jean-Pierre Eckmann

Abstract

It has been recognized in the last few years that dynamical systems with few degrees of freedom can play an important role in the description of some physical systems which behave in a chaotic way. The rather simple one dimensional dynamical systems can also be used to test some ideas about higher dimensional systems. The question of the statistical description of chaotic motions was already raised several decades ago ([U]) and after the discovery of the ergodic theorems it became obvious that an important notion is that of invariant measure. For a given dynamical system, there are in general many invariant measures, and one is led to the problem of choosing the relevant one (if any).

Keywords

Entropy 

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Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Pierre Collet
    • 1
  • Jean-Pierre Eckmann
    • 2
  1. 1.Centre de Physique ThéoriqueEcole PolytechniquePalaiseau CedexFrance
  2. 2.Dept. de Physique ThéoriqueGenève 4Suisse

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