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

Ja G. Sinai, E. B. Vul

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)27-47
Number of pages21
JournalJournal of Statistical Physics
Issue number1
StatePublished - Jul 1980

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Poincaré mapping
  • attractor
  • closed orbit
  • linear system of equations in variations


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