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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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
|Deposited By:||Thomas Wagenknecht|
|Deposited On:||14 August 2007|