A higher dimensional generalization of Bendixon's criterion

A. Pogromsky; G. Leonov; H. Nijmeijer

doi:10.3182/20020721-6-es-1901.00289

A higher dimensional generalization of Bendixon's criterion

A. Pogromsky, G. Leonov, H. Nijmeijer

Dynamics and Control

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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.

Originele taal-2	Engels
Pagina's (van-tot)	235-240
Aantal pagina's	6
Tijdschrift	IFAC Proceedings Volumes
Volume	35
Nummer van het tijdschrift	1
DOI's	https://doi.org/10.3182/20020721-6-es-1901.00289
Status	Gepubliceerd - 2002
Evenement	15th World Congress of the International Federation of Automatic Control (IFAC 2002 World Congress) - Barcelona, Spanje Duur: 21 jul. 2002 → 26 jul. 2002 Congresnummer: 15

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10.3182/20020721-6-es-1901.00289

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abstract = "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.",

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AB - 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.

KW - Direct Lyapunov method

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KW - Periodic solutions

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A higher dimensional generalization of Bendixon's criterion

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