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Journal of Statistical Physics

, Volume 23, Issue 1, pp 27–47 | Cite as

Discovery of closed orbits of dynamical systems with the use of computers

  • Ja. G. Sinai
  • E. B. Vul
Articles

Abstract

In this paper we derive a general criterion which can be used for the discovery with the use of a computer of closed orbits of systems of ordinary differential equations. We apply this criterion to the Lorenz model and show rigorously the existence of a closed orbit for the case under consideration. In a subsequent paper we shall show how the stable manifold of this orbit determines the boundary of the stochastic attractor.

Key words

Poincaré mapping linear system of equations in variations closed orbit attractor 

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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Ja. G. Sinai
    • 1
  • E. B. Vul
    • 1
  1. 1.Landau Institute of Theoretical PhysicsAcademy of SciencesMoscowUSSR

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