Symplectic Blenders and Persistence of Homoclinics to Saddle-Center Periodic Orbits

Symplectic Blenders and Persistence of Homoclinics to Saddle-Center Periodic Orbits

Explore a 49-minute lecture on symplectic blenders and their role in the persistence of homoclinic intersections for saddle-center periodic orbits. Delve into the concept of blenders as hyperbolic basic sets with unremovable non-transverse intersections of invariant manifolds. Examine the existence of symplectic blenders near one-dimensional whiskered tori with homoclinic tangencies in C^r symplectic diffeomorphisms. Discover how this result leads to the persistence of non-transverse homoclinic intersections for generic saddle-center periodic orbits in both symplectic diffeomorphisms and Hamiltonian systems. Gain insights into the C^r boundary of C^1 open regions where systems with such homoclinic intersections are dense.