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

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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.

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iv, 102 leaves : ill.

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Richardson, Peter A. (Peter Adolph), 1955- December 1998.

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  • Richardson, Peter A. (Peter Adolph), 1955-

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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.

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iv, 102 leaves : ill.

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  • December 1998

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  • March 26, 2014, 9:30 a.m.

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  • July 29, 2014, 9:54 a.m.

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Richardson, Peter A. (Peter Adolph), 1955-. Natural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical Systems, dissertation, December 1998; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc278917/: accessed August 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .