Families of multi-round homoclinic and periodic orbits near a saddle-center equilibrium

Regular and Chaotic Dynamics

Volumn 8, Issue 2, 2003, Pages 191-200

  Koltsova, O Yu ^a  

^a LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

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EID: 34548700917     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2003v008n02ABEH000240     Document Type: Article

References (7)

1. C. Grotta Ragazzo. Irregular dynamics and Homoclinic Orbits to Hamiltonian Saddle-Center. Comm. Pure Appl. Math. Phys. V. L. 1997. P. 105-147.
2. O. Yu. Koltsova. On a structure of a bifurcation set in a two-parameter family of Hamiltonian systems with a seperatrix loop, in Methods of Qualitative Theory of Diff. Eq. Ed. L. P. Shil'nikov. 1991. P. 25-35. (In Russian)
3. O. Yu. Koltsova, L. M. Lerman. Periodic and homoclinic orbits in a two-parameter unfolding of a Hamiltonian systems with a homoclinic orbit to a saddle-center. Int. J. of Bifurcations and Chaos. V. 5, 2. 1995. P. 397-408.
4. L. M. Lerman. Hamiltonian systems with a separatrix loop of a saddle-center. In "Methods of Qualitative Theory of Diff. Eq". Ed. E. A. Leontovich-Andronova. 1987. P. 89-103.
5. (In Russian. (Engl.transl. in Selecta Math. Sov. 10, 297, (1991))).
6. A. Mielke, P.Holmes, O. O'Reilly. Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center. J. Dyn. Diff. Eq. V. 4. 1992. P. 95-126.
7. J. Moser. On the generalization of a theorem of A. Liapunoff. Comm. Pure Appl. Math. V. 11. 1958. P. 257-271.