Speaker: Sajjad Bakrani (Imperial College London).

Abstract: Consider a Hamiltonian flow on R4 with a hyperbolic equilibrium O and a transverse homoclinic orbit Gamma. In this talk, we discuss the dynamics near Gamma in its energy level when it leaves and enters O along strong unstable and strong stable directions, respectively. In particular, we introduce necessary and sufficient conditions for the existence of the local stable and unstable invariant manifolds of Gamma. We then consider the case in which both of these manifolds exist. We globalize them and assume they intersect transversely. We show that near any orbit of this intersection, called super-homoclinic, there exist infinitely many multi-pulse homoclinic loops.

Zoom Meeting: https://videoconf-colibri.zoom.us/j/98242649197.