Homoclinic Chaos in Generalized Henon-Heiles System
S. Kasperczuk
Institute of Physics, Pedagogical University, Pl. Słowiański 6, 65-069 Zielona Góra, Poland
Received: June 27, 1995
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This paper considers the generalized Henon-Heiles system, defined by the Hamiltonian Η = (p21 + p22 + Αq21 + Bq22)/2 + Cq21q2 + Dq32. Melnikov's method is used to prove the existence of nondegenerate homoclinic orbits near two integrable cases: (o) C = 0; A, B, D arbitrary; (i) A = B; C = 3D. The existence of such orbits precludes the existence of analytic second integrals.
DOI: 10.12693/APhysPolA.88.1073
PACS numbers: 05.45.+b