Higher-order Melnikov method and chaos for two-degree-of-freedom Hamiltonian systems with saddle-centers | Zendy

Kazuyuki Yagasaki | Zendy

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Higher-order Melnikov method and chaos for two-degree-of-freedom Hamiltonian systems with saddle-centers

Author(s) -

Kazuyuki Yagasaki

Publication year - 2010

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2011.29.387

Subject(s) - homoclinic orbit , saddle , hamiltonian system , chaotic , mathematics , degree (music) , classical mechanics , order (exchange) , hamiltonian (control theory) , mathematical analysis , chaos (operating system) , physics , mathematical physics , bifurcation , nonlinear system , computer science , quantum mechanics , mathematical optimization , computer security , finance , acoustics , economics , artificial intelligence

We consider two-degree-of-freedom Hamiltonian systems with saddle-centers, and develop a Melnikov-type technique for detecting creation of transverse homoclinic orbits by higher-order terms. We apply the technique to the generalized Henon-Heiles system and give a positive answer to a remaining question of whether chaotic dynamics occurs for some parameter values although it is known to be nonintegrable in a complex analytical meaning.

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