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Dynamical Features in a Slow-fast Piecewise Linear Hamiltonian System

Published online by Cambridge University Press:  17 September 2013

A. Kazakov
Affiliation:
Lobachevsky State University of Nizhni Novgorod, Russia
N. Kulagin
Affiliation:
The State University of Management, Moscow, Russia
L. Lerman*
Affiliation:
Lobachevsky State University of Nizhni Novgorod, Russia
*
Corresponding author. E-mail: lermanl@mm.unn.ru
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Abstract

We demonstrate that a piecewise linear slow-fast Hamiltonian system with an equilibrium of the saddle-center type can have a sequence of small parameter values for which a one-round homoclinic orbit to this equilibrium exists. This contrasts with the well-known findings by Amick and McLeod and others that solutions of such type do not exist in analytic Hamiltonian systems, and that the separatrices are split by the exponentially small quantity. We also discuss existence of homoclinic trajectories to small periodic orbits of the Lyapunov family as well as symmetric periodic orbits near the homoclinic connection. Our further result, illustrated by simulations, concerns the complicated structure of orbits related to passage through a non-smooth bifurcation of a periodic orbit.

Type
Research Article
Copyright
© EDP Sciences, 2013

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