00-51 Maciej P. Wojtkowski.

W -- Flows on Weyl Manifolds and Gaussian Thermostats. (76K, AMS-TEX) Feb 1, 00

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 00-51.tex