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

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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. 
@article{ZNSL_2003_300_a17,
     author = {O. Yu. Koltsova},
     title = {On {Hamiltonian} systems with homoclinic orbit to a~saddle-center},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {187--193},
     publisher = {mathdoc},
     volume = {300},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a17/}
}
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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/