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Dynamical Features in a Slow-fast Piecewise Linear HamiltonianSystem

Published online by Cambridge University Press:  17 September 2013

A. Kazakov ,
N. Kulagin  and
L. Lerman
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 equilibriumof the saddle-center type can have a sequence of small parameter values for which aone-round homoclinic orbit to this equilibrium exists. This contrasts with the well-knownfindings by Amick and McLeod and others that solutions of such type do not exist inanalytic Hamiltonian systems, and that the separatrices are split by the exponentiallysmall quantity. We also discuss existence of homoclinic trajectories to small periodicorbits of the Lyapunov family as well as symmetric periodic orbits near the homoclinicconnection. Our further result, illustrated by simulations, concerns the complicatedstructure of orbits related to passage through a non-smooth bifurcation of a periodicorbit.

Keywords

slow-fast systemHamiltonianpiecewise linearhomoclinicperiodicnonsmooth bifurcation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 5: Bifurcations , 2013 , pp. 155 - 172
Copyright
© EDP Sciences, 2013

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