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Communications in Mathematical Physics

, Volume 214, Issue 3, pp 573–592 | Cite as

Homotopy Classes for Stable Periodic and Chaotic¶Patterns in Fourth-Order Hamiltonian Systems

  • W.D. Kalies
  • J. Kwapisz
  • J.B. VandenBerg
  • R.C.A.M. VanderVorst

Abstract:

We investigate periodic and chaotic solutions of Hamiltonian systems in ℝ4 which arise in the study of stationary solutions of a class of bistable evolution equations. Under very mild hypotheses, variational techniques are used to show that, in the presence of two saddle-focus equilibria, minimizing solutions respect the topology of the configuration plane punctured at these points. By considering curves in appropriate covering spaces of this doubly punctured plane, we prove that minimizers of every homotopy type exist and characterize their topological properties.

Keywords

Evolution Equation Stationary Solution Hamiltonian System Topological Property Variational Technique 
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 Berlin Heidelberg 2000

Authors and Affiliations

  • W.D. Kalies
    • 1
  • J. Kwapisz
    • 2
  • J.B. VandenBerg
    • 3
  • R.C.A.M. VanderVorst
    • 3
  1. 1.Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA.¶E-mail: wkalies@fau.eduUS
  2. 2.Department of Mathematical Sciences, Montana State University-Bozeman, Bozeman, MT 59717-2400, USA.¶E-mail: jarek@math.montana.eduUS
  3. 3.Department of Mathematical Sciences, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden,¶The Netherlands. E-mail: gvdberg@math.leidenuniv.nl; vanderv@math.leidenuniv.nlNL

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