Generalized Hamilton flow and poisson relation for the scattering kernel

The generalized Hamilton how determined by a Hamilton function on a symplec tic manifold with boundary is considered. A regularity property of this flo w is proved, which for "Sard's theorem type applications" is as good as smo othness. it implies in particular that the generalized Hamilton flow preser ves the Hausdorff dimension of Borel subsets of its phase space. As an appl ication, it is shown that in scattering by obstacles, the so-called Poisson relation for the scattering kernel s(t, theta, omega) becomes an equality for almost all pairs of unit vectors (theta, omega). (C) 2000 Editions scie ntifiques et me'dicaIes Elsevier SAS.