题目：Topological instability in analytic Hamiltonian systems
摘要：In this talk, I will mainly discuss the instability phenomenon under the effect of small real-analytic Hamiltonian perturbations. With a general geometric mechanism, we can construct local diffusing trajectories (i.e. the slow action variables drift by a quantity of order 1) in a priori unstable Hamiltonian systems of arbitrary n>2 degrees of freedom. We also prove that such an evolution occurs under a generic (i.e. open-dense) real-analytic perturbation. This is joint work with R. de la Llave.