山田淳二 氏
2017年1月12日(木) 15時00分
総合研究10号館317号室(セミナー室)
A geodesic can be represented by a Hamiltonian vector field, and its flow is called a geodesic flow. We consider geodesics on a perturbed surface of revolution which represent holonomic dynamical systems on three-dimensional space. The Hamiltonian systems of geodesic flows on surfaces of revolution have homo/heteroclinic orbits. We apply Melnikov’s method to the Hamiltonian vector field, and show the transversality of the homo/heteroclinic orbits.[1] S. V. Bolotin, P. H. Rabinowitz, Minimal heteroclinic geodesics for the n-torus, Calc. Var. 9 (1999), 125-139.
[2] K. Burns, H. Weiss, A Geometric Criterion for Positive Topological Entropy, Commun. Math. Phys. 172 (1995), 95-118.
[3] S. Wiggins, Global Bifurcations and Chaos, (1988), 334-418.