Chaos in Perturbed Planan Non-Hamiltonian Integrable Systems with Slowly-Varying Angle Parameters

CHEN Li-qun

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CHEN Li-qun. Chaos in Perturbed Planan Non-Hamiltonian Integrable Systems with Slowly-Varying Angle Parameters[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1172-1176.

Citation:

CHEN Li-qun. Chaos in Perturbed Planan Non-Hamiltonian Integrable Systems with Slowly-Varying Angle Parameters[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1172-1176.

Citation:

CHEN Li-qun. Chaos in Perturbed Planan Non-Hamiltonian Integrable Systems with Slowly-Varying Angle Parameters[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1172-1176.

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Chaos in Perturbed Planan Non-Hamiltonian Integrable Systems with Slowly-Varying Angle Parameters

CHEN Li-qun

Department of Mechanics, Shanghai University;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China

Received Date: 2000-07-19
Rev Recd Date: 2001-04-08
Publish Date: 2001-11-15

Abstract

Abstract

The Melnikov method was extended to perturbed planan non-Hamiltonian integrable systems with slowly-varying angle parameters.Based on the analysis of the geometric structure of unperturbed systems,the condition of transversely homoclinic intersection was established.The generalized Melnikov function of the perturbed system was presented by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.Chaos may occur in the system if the generalized Melnikov function has simple zeros.
- Melnikov method,
- perturbed integrable system,
- transversely homoclinic,
- chaos

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References(8)

References

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