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 geometric properties of the system's phase space. In particular,
these results hold for a fairly nonrestrictive class of triangular configurations of
scatterers.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc278917 |
| Date | 12 1900 |
| Creators | Richardson, Peter A. (Peter Adolph), 1955- |
| Contributors | Mauldin, R. Daniel, Urbański, Mariusz, Neuberger, J. W. (John W.), 1934-, Chernov, Nikolai, 1956- |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iv, 102 leaves : ill., Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Richardson, Peter A. (Peter Adolph), 1955- |
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