Geodesic
Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation
Russian journal of nonlinear dynamics, Tome 15 (2019) no. 2, pp. 187-198

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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, separatrix manifolds.
Mots-clés : limit cycles 
@article{ND_2019_15_2_a7,
     author = {A. D. Morozov and K. E. Morozov},
     title = {Global {Dynamics} of {Systems} {Close} to {Hamiltonian} {Ones} {Under} {Nonconservative} {Quasi-periodic} {Perturbation}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {187--198},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2019_15_2_a7/}
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A. D. Morozov; K. E. Morozov. Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation. Russian journal of nonlinear dynamics, Tome 15 (2019) no. 2, pp. 187-198. http://geodesic.mathdoc.fr/item/ND_2019_15_2_a7/