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Natural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical Systems

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.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc278917
Date12 1900
CreatorsRichardson, Peter A. (Peter Adolph), 1955-
ContributorsMauldin, R. Daniel, UrbaƄski, Mariusz, Neuberger, J. W. (John W.), 1934-, Chernov, Nikolai, 1956-
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formativ, 102 leaves : ill., Text
RightsPublic, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Richardson, Peter A. (Peter Adolph), 1955-

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