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2007.102: Snaking of multiple homoclinic orbits in reversible systems

2007.102: J. Knobloch and T. Wagenknecht (2007) Snaking of multiple homoclinic orbits in reversible systems.

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Abstract

We study N-homoclinic orbits near a heteroclinic cycle in a reversible system. The cycle is assumed to connect two equilibria of saddle-focus type. Using Lin's method we establish the existence of infinitely many N-homoclinic orbits for each N near the cycle. In particular, these orbits exist along snaking curves, thus mirroring the behaviour one-homoclinic orbits. The general analysis is illustrated by numerical studies for a Swift-Hohenberg system.

Item Type:MIMS Preprint
Subjects:MSC 2000 > 34 Ordinary differential equations
MSC 2000 > 37 Dynamical systems and ergodic theory
MIMS number:2007.102
Deposited By:Thomas Wagenknecht
Deposited On:14 August 2007

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