We study the dynamics of a multidimensional slow-fast Hamiltonian system in a
neighborhood of the slow manifold under the assumption that the frozen system has a hyperbolic
equilibrium with complex simple leading eigenvalues and there exists a transverse homoclinic
orbit. We obtain formulas for the corresponding Shilnikov separatrix map and prove the
existence of trajectories in a neighborhood of the homoclinic set with a prescribed evolution of
the slow variables. An application to the 3 body problem is given.
Keywords:
Hamiltonian system, homoclinic orbit, Poincaré function, separatrix map
Citation:
Bolotin S. V., Dynamics of Slow-Fast Hamiltonian Systems: The Saddle-Focus Case, Regular and Chaotic Dynamics,
2025, Volume 30, Number 1,
pp. 76-92