THE SYMPLECTIC STUDY OF MOTIONS IN A PERTURBED VAN-DER-POL DYNAMICAL SYSTEM


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Abstract

We study a weakly perturbed van-der-Pol dynamical system and the structure of its trajectory behavior via the modern symplectic theory. Based on a Samoilenko–Prykarpatsky method of studying integral submanifolds of weakly perturbed completely integrable Hamiltonian systems, we prove the regularity of deformations of the Lagrangian asymptotic submanifolds in a vicinity of the hyperbolic periodic orbit.

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