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Watch a mathematics research lecture exploring how Zehnder's theorem on transverse homoclinic orbits in disk maps can be adapted to prove the existence of periodic orbits with transverse homoclinic intersections in generic analytic strongly convex billiards. Learn about an ongoing research project that combines Zehnder's strategic approach with Aubry-Mather theory for twist maps to demonstrate that for any rational rotation number, generic analytic strongly convex billiards possess periodic orbits featuring transverse homoclinic intersections. Delivered as part of the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" at the Erwin Schrödinger International Institute, this technical presentation delves into the mathematical foundations connecting area-preserving disk maps and billiard dynamics through the lens of homoclinic orbit theory.
