00-51 Maciej P. Wojtkowski.
W -- Flows on Weyl Manifolds and Gaussian Thermostats. (76K, AMS-TEX) Feb 1, 00
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Abstract. We introduce W-flows, 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 W-flows, 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 W-flows 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{Ch-E-L-S}, is uniformly hyperbolic, if only \$r|E| < 1\$, and this condition is sharp.

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