Flow-Invariant Hypersurfaces in Semi-Dispersing Billiards |
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Authors: | Nikolai Chernov Nandor Simányi |
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Institution: | (1) Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA |
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Abstract: | This work results from our attempts to solve Boltzmann–Sinai’s hypothesis about the ergodicity of hard ball gases. A crucial
element in the studies of the dynamics of hard balls is the analysis of special hypersurfaces in the phase space consisting
of degenerate trajectories (which lack complete hyperbolicity). We prove that if a flow-invariant hypersurface J in the phase space of a semi-dispersing billiard has a negative Lyapunov function, then the volume of the forward image of
J grows at least linearly in time. Our proof is independent of the solution of the Boltzmann–Sinai hypothesis, and we provide
a complete and self-contained argument here.
Submitted: March 14, 2006. Accepted: August 2, 2006. |
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Keywords: | |
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