Communications in Mathematical Physics

, Volume 131, Issue 3, pp 605–617 | Cite as

At the other side of a saddle-node

  • M. Misiurewicz
  • A. L. Kawczyński
Article

Abstract

We describe phenomena occurring just before a saddle-node bifurcation for one-parameter families of interval maps. In particular, as a parameter approaches the bifurcation value, attracting periodic orbits of periodsk, k+1,k+2,k+3,... can appear. We make a detailed study of a family of “cusp-shaped” maps, where this phenomenon occurs in a pure form.

Keywords

Neural Network Statistical Physic Complex System Periodic Orbit Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • M. Misiurewicz
    • 1
  • A. L. Kawczyński
    • 2
  1. 1.Institute of MathematicsWarsaw University, PKiNIX p.WarszawaPoland
  2. 2.Institute of Physical ChemistryPolish Academy of SciencesWarszawaPoland

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