# Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton–Jacobi equation

@article{Delshams2011TransversalityOH,
title={Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton–Jacobi equation},
author={Amadeu Delshams and Pere Guti'errez and Juan R. Pacha},
journal={Physica D: Nonlinear Phenomena},
year={2011},
volume={243},
pages={64-85}
}
• Published 30 December 2011
• Mathematics
• Physica D: Nonlinear Phenomena
Abstract We consider a Hamiltonian system with 2 degrees of freedom, with a hyperbolic equilibrium point having a loop or homoclinic orbit (or, alternatively, two hyperbolic equilibrium points connected by a heteroclinic orbit), as a step towards understanding the behavior of nearly-integrable Hamiltonians near double resonances. We provide a constructive approach to study whether the unstable and stable invariant manifolds of the hyperbolic point intersect transversely along the loop, inside…
2 Citations

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