Communications in Mathematical Physics

, Volume 72, Issue 1, pp 49–53 | Cite as

On a normal form of symmetric maps of [0, 1]

  • H. Rüssmann
  • E. Zehnder


A class of continuous symmetric mappings of [0, 1] into itself is considered leaving invariant a measure absolutely continuous with respect to the Lebesgue measure.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Normal Form 
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  1. 1.
    Ruelle, D.: Applications conservant une mesure absolument continue par rapport adx sur [0,1]. Commun. Math. Phys.55, 47–51 (1977)Google Scholar
  2. 2.
    Lasota, A., Yorke, J.A.: On the existence of invariant measures for piecewise monotonic transformations. Trans. Am. Math. Soc.186, 481–488 (1973)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • H. Rüssmann
    • 1
  • E. Zehnder
    • 2
  1. 1.Fachbereich Mathematik der Johannes GutenbergUniversität MainzMainz
  2. 2.Mathematisches Institut der Ruhr-Universität BochumBochumGermany

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