Weak H¨older Continuity of the Generalized Hamiltonian Flow

The generalized Hamiltonian flow Ft generated by a smooth function on a symplectic manifold S with smooth boundary ­ S is considered. It is proved that if Ft has no tangencies of infinite order to ­ S, then given a metric d on S, an integral curve s t. of Ft , a compact neighbourhood K of s 0. in S, and T)0, there exist a)0 and C)0 such that d s t., r t..FCd s 0., r 0..a holds for