A higher dimensional generalization of Bendixon's criterion

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Conditions are given that guarantee the nonexistence of periodic orbits lying entirely in a simply connected set. The conditions are formulated in terms of matrix inequalities involving the variational equation. For systems defined in R the conditions are equivalent to Bendixon's criterion. A connection with analytic estimates of the Hausdorff dimension of invariant compact sets is emphasized.

Original languageEnglish
Pages (from-to)235-240
Number of pages6
JournalIFAC Proceedings Volumes
Issue number1
Publication statusPublished - 2002
Event15th World Congress of the International Federation of Automatic Control (IFAC 2002 World Congress) - Barcelona, Spain
Duration: 21 Jul 200226 Jul 2002
Conference number: 15


  • Direct Lyapunov method
  • Linearization
  • Periodic solutions


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