 0051 Maciej P. Wojtkowski.
 W  Flows on Weyl Manifolds and Gaussian Thermostats.
(76K, AMSTEX)
Feb 1, 00

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Abstract. We introduce Wflows, by modifying the geodesic flow on a Weyl
manifold, and show that they coincide with the isokinetic dynamics. We
establish some connections between negative curvature of the Weyl
structure and the hyperbolicity of Wflows, generalizing in dimension
2 the classical result of Anosov on Riemannian geodesic flows. In
higher dimensions we establish only weaker hyperbolic properties. We
extend the theory to billiard Wflows and introduce the Weyl
counterparts of Sinai billiards. We obtain that the isokinetic
Lorentz gas with the constant external field $E$ and scatterers of
radius $r$, studied by Chernov, Eyink, Lebowitz and Sinai in
\cite{ChELS}, is uniformly hyperbolic, if only $rE < 1$, and this
condition is sharp.
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