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Nelin. Dinam., 2019, Volume 15, Number 2, Pages 187–198 (Mi nd652)  

Mathematical problems of nonlinearity

Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation

A. D. Morozov, K. E. Morozov

Lobachevsky State University of Nizhni Novgorod, prosp. Gagarina 23, Nizhni Novgorod 603950, Russia

Abstract: We study quasi-periodic nonconservative perturbations of two-dimensional Hamiltonian systems. We suppose that there exists a region $D$ filled with closed phase curves of the unperturbed system and consider the problem of global dynamics in $D$. The investigation includes examining the behavior of solutions both in $D$ (the existence of invariant tori, the finiteness of the set of splittable energy levels) and in a neighborhood of the unperturbed separatrix (splitting of the separatrix manifolds). The conditions for the existence of homoclinic solutions are stated. We illustrate the research with the Duffing – Van der Pole equation as an example.

Keywords: resonances, quasi-periodic, periodic, averaged system, phase curves, equilibrium states, limit cycles, separatrix manifolds

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00306
Ministry of Education and Science of the Russian Federation 1.3287.2017/PCh
Russian Science Foundation 19-11-00280
This work has been partially supported by the Russian Foundation for Basic Research under grant no. 18-01-00306, by the Ministry of Education and Science of the Russian Federation (project no. 1.3287.2017/PCh) and by the Russian Science Foundation under grant no. 19-11-00280.


DOI: https://doi.org/10.20537/nd190208

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MSC: 34C15, 34C27, 34C37
Received: 14.04.2019
Accepted:20.06.2019

Citation: A. D. Morozov, K. E. Morozov, “Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation”, Nelin. Dinam., 15:2 (2019), 187–198

Citation in format AMSBIB
\Bibitem{MorMor19}
\by A. D. Morozov, K. E. Morozov
\paper Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 2
\pages 187--198
\mathnet{http://mi.mathnet.ru/nd652}
\crossref{https://doi.org/10.20537/nd190208}


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