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On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems

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Title: On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems
Authors: Giles, W
Lamb, J
Turaev, D
Item Type: Journal Article
Abstract: We consider a Hamiltonian system which has an elliptic-hyperbolic equilibrium with a homoclinic loop. We identify the set of orbits which are homoclinic to the center manifold of the equilibrium via a Lyapunov- Schmidt reduction procedure. This leads to the study of a singularity which inherits certain structure from the Hamiltonian nature of the system. Under non-degeneracy assumptions, we classify the possible Morse indices of this singularity, permitting a local description of the set of homoclinic orbits. We also consider the case of time-reversible Hamiltonian systems.
Issue Date: 26-Aug-2016
Date of Acceptance: 21-Jun-2016
URI: http://hdl.handle.net/10044/1/41911
DOI: https://dx.doi.org/10.1088/0951-7715/29/10/3148
ISSN: 1361-6544
Publisher: IOP Publishing
Journal / Book Title: Nonlinearity
Volume: 29
Copyright Statement: ©2016 IOP Publishing Ltd.
Keywords: math.DS
General Mathematics
0102 Applied Mathematics
Publication Status: Published
Article Number: 3148
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences