Homoclinic Chaos in Generalized Henon-Heiles System |

S. KasperczukInstitute 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 = (p^{2}_{1} + p^{2}_{2} + Αq^{2}_{1} + Bq^{2}_{2})/2 + Cq^{2}_{1}q_{2} + Dq^{3}_{2}. 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 |