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Zbl 1112.37319
Koltsova, O. Yu.
Families of multi-round homoclinic and periodic orbits near a saddle-center equilibrium. (English)
[J] Regul. Chaotic Dyn. 8, No. 2, 191-200 (2003). ISSN 1560-3547; ISSN 1468-4845/e

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 2000:: *37J45 Periodic, homoclinic and heteroclinic orbits, etc.
37C29 Homoclinic and heteroclinic orbits
37J20 Bifurcation problems

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