Communications in Mathematical Physics

, Volume 76, Issue 3, pp 211–254 | Cite as

Universal properties of maps on an interval

  • P. Collet
  • J. -P. Eckmann
  • O. E. LanfordIII
Article

Abstract

We consider itcrates of maps of an interval to itself and their stable periodic orbits. When these maps depend on a parameter, one can observe period doubling bifurcations as the parameter is varied. We investigate rigorously those aspects of these bifurcations which are universal, i.e. independent of the choice of a particular one-parameter family. We point out that this universality extends to many other situations such as certain chaotic regimes. We describe the ergodic properties of the maps for which the parameter value equals the limit of the bifurcation points.

Keywords

Neural Network Statistical Physic Complex System Periodic Orbit Nonlinear Dynamics 
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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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • P. Collet
    • 1
  • J. -P. Eckmann
    • 2
  • O. E. LanfordIII
    • 3
  1. 1.Harvard UniversityCambridgeUSA
  2. 2.Département de Physique ThéoriqueUniversité de GenèveGenève 4Switzerland
  3. 3.University of CaliforniaBerkeleyUSA

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