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Complex dynamics and bifurcations in a Hamiltonian system having a transversal homoclinic orbit to a saddle focus.

A Hamiltonian system having a saddle-focus singular point with a transversal homoclinic orbit is considered. The bifurcations that occur upon a variation of the Hamiltonian are studied. Reconstructions of a symbolic system describing the hyperbolic set are investigated. Bifurcations linked with the appearance of Smale horseshoes are pointed out. The results are applied to a system determining traveling-wave solutions of the Landau-Lifshitz equation. Multisolitons with any number of humps can exist.