Action-minimizing Methods in Hamiltonian Dynamics

An Introduction to Aubry-Mather Theory

af Alfonso Sorrentino

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach--known as Aubry-Mather theory--singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics ... (Læs mere)