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Periodic Solutions, Stability and Non-Integrability in a Generalized Hénon-Heiles Hamiltonian System
2013
Journal of Nonlinear Mathematical Physics
We consider the Hamiltonian function defined by the cubic polynomial H = 1 2 (p 2 x + p 2 y ) + 1 2 (x 2 + y 2 ) + A 3 x 3 + Bxy 2 + Dx 2 y, where A, B, D ∈ R are parameters and so H is an extension of the well known Hénon-Heiles problem. Our main contribution for D = 0, A + B = 0 and other technical restrictions are in three aspects: existence of periodic solutions, stability and instability of these periodic solutions and the problem of nonintegrability of the system associated to H.
doi:10.1080/14029251.2013.805567
fatcat:7pma6ffesjfafjbxx7m5ka4t5y