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

    Received 14 April 2019; accepted 20 June 2019

    2019, Vol. 15, no. 2, pp.  187-198

    Author(s): Morozov A. D., Morozov K. E.

    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
    Citation: Morozov A. D., Morozov K. E., Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 2, pp.  187-198

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