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Perturbed generalised Hamiltonian systems and some advection models

Published online by Cambridge University Press:  17 April 2009

Jibin Li ,
J.R. Christie  and
K. Gopalsamy
Jibin Li
Affiliation:
Institute of Applied Maths of Yunnan ProvinceDepartment of MathematicsKunming University of Science & TechnologyYunnan 650093People's Republic of China e-mail: [email protected]
J.R. Christie
Affiliation:
Department of Mathematics and StatisticsThe Flinders University of South AustraliaGPO Box 2100Adelaide SA 5001Australia e-mail: [email protected]
K. Gopalsamy
Affiliation:
Department of Mathematics and StatisticsThe Flinders University of South AustraliaGPO Box 2100Adelaide SA 5001Australia e-mail: [email protected]
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Abstract

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In this paper, it is shown that the theory of perturbed generalised Hamiltonian systems provides an effective method for understanding the description of flow patterns of some three-dimensional flows. Firstly, theorems for the persistence of periodic solutions of three-dimensional generalised Hamiltonian systems under perturbation are given by developing Melnikov's method. Then, three different systems of three-dimensional steady fluid flows are discussed and the existence or non-existence of periodic solutions of these systems is proved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 1 - 24
Copyright
Copyright © Australian Mathematical Society 1998

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