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Families of multi-round homoclinic and periodic orbits near a saddle-center equilibrium. (English) Zbl 1112.37319
Summary: We consider a real analytic two degrees of freedom Hamiltonian system possessing a homoclinic orbit to a saddle-center equilibrium p (two nonzero real and two nonzero imaginary eigenvalues). We take a two-parameter unfolding for such a system and show that in the case of nonresonance there are countable sets of multi-round homoclinic orbits to p. We also find families of periodic orbits, accumulating the homoclinic orbits.
MSC:
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
37C29Homoclinic and heteroclinic orbits
37J20Bifurcation problems (finite-dimensional Hamiltonian etc. systems)