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 R2 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
Title of host publication15th Triennial World Congress of the International Federation of Automatic Control
Place of PublicationSpain, Barcelona
Publication statusPublished - 2002


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