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

  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},
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… 

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