Geodesic
On Hamiltonian systems with homoclinic orbit to a saddle-center
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 187-193 
O. Yu. Koltsova. On Hamiltonian systems with homoclinic orbit to a saddle-center. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 187-193. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a17/
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     author = {O. Yu. Koltsova},
     title = {On {Hamiltonian} systems with homoclinic orbit to a~saddle-center},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a17/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider a real analytic two degrees of freedom Hamiltonian system possessing a homoclinic orbit to a saddle-center equilibrium (two nonzero real and two nonzero imaginary eigenvalues). We take a two-parameter unfolding for such the system and show that in nonresonance case there are countable sets of multi-round homoclinic orbits to a saddle-center. We also find families of periodic orbits, accumulating at homoclinic orbits.

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