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

Kazuyuki Yagasaki
2010 Discrete and Continuous Dynamical Systems. Series A  
We consider two-degree-of-freedom Hamiltonian systems with saddlecenters, and develop a Melnikov-type technique for detecting creation of transverse homoclinic orbits by higher-order terms. We apply the technique to the generalized Hénon-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.
doi:10.3934/dcds.2011.29.387 fatcat:koyfgyvcm5b5dltms4rlvy2zoi