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arXiv · 1512.02148

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

William Giles·Jeroen Lamb·Dmitry Turaev
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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.

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William Giles, Jeroen Lamb, Dmitry Turaev. 2015-12-07. On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems. https://doi.org/10.1088/0951-7715%2F29%2F10%2F3148

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