Natural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical Systems
Description:
In this paper, we prove, for a certain class of open billiard dynamical systems, the existence of a family of smooth probability measures on the leaves of the dynamical system's unstable manifold. These measures describe the conditional asymptotic behavior of forward trajectories of the system. Furthermore, properties of these families are proven which are germane to the PYC programme for these systems. Strong sufficient conditions for the uniqueness of such families are given which depend upon…
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Date:
December 1998
Creator:
Richardson, Peter A. (Peter Adolph), 1955-