Hamiltonian C-0-continuity of Lagrangian capacity on the cotangent bundle

Abstract

Partially motivated by the study of topological Hamiltonian dynamics, we prove the following C-0-continuity of the Lagrangian capacity function gamma(lag): gamma l(ag) (phi(1)(H)(0N)) := p(lag) (H;1) - p(lag) (H; [pt](#) -> 0 as phi(1)(H) -> id, provided the H's satisfy supp X-H subset of D-R(T*N) \ (0B) for some R> 0 and a closed subset B subset of N with nonempty interior. We also provide an estimate of the capacity in terms of the C-0-distance of d(C)0 (phi(1)(H), id) and the subset B subset of N relative to T*N.