Localization/nonuniqueness problems for periodic orbits of polynomial autonomous systems

Konstantin E. Starkov

Localization/nonuniqueness problems for periodic orbits of polynomial autonomous systems

Research output: Contribution to conference › Paper › peer-review

Abstract

In this paper we present sufficient conditions guaranteeing that a polynomial autonomous system has a periodic orbit Γ₁ passing through some point x₁ provided there is another point x₂ which is contained in some periodic orbit Γ₂. We consider two cases: the case of equal minimal periods and the case of nonequal periods. Our approach described for periodic orbits is applied to polynomial autonomous systems with homoclinic orbits and heteroclinic orbits as well. One example is examined.

Original language	English
Pages	303-306
Number of pages	4
State	Published - 2000
Externally published	Yes
Event	2nd Interntional Conference on Control of Oscillations and Chaos (COC 2000) - ST. Petersbug, Russia Duration: 5 Jul 2000 → 7 Jul 2000

Conference

Conference	2nd Interntional Conference on Control of Oscillations and Chaos (COC 2000)
City	ST. Petersbug, Russia
Period	5/07/00 → 7/07/00

Cite this

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abstract = "In this paper we present sufficient conditions guaranteeing that a polynomial autonomous system has a periodic orbit Γ1 passing through some point x1 provided there is another point x2 which is contained in some periodic orbit Γ2. We consider two cases: the case of equal minimal periods and the case of nonequal periods. Our approach described for periodic orbits is applied to polynomial autonomous systems with homoclinic orbits and heteroclinic orbits as well. One example is examined.",

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AB - In this paper we present sufficient conditions guaranteeing that a polynomial autonomous system has a periodic orbit Γ1 passing through some point x1 provided there is another point x2 which is contained in some periodic orbit Γ2. We consider two cases: the case of equal minimal periods and the case of nonequal periods. Our approach described for periodic orbits is applied to polynomial autonomous systems with homoclinic orbits and heteroclinic orbits as well. One example is examined.

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SP - 303

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T2 - 2nd Interntional Conference on Control of Oscillations and Chaos (COC 2000)

Y2 - 5 July 2000 through 7 July 2000

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Localization/nonuniqueness problems for periodic orbits of polynomial autonomous systems

Abstract

Conference

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