- 05-327 Chernov N.
- Regularity of local manifolds in dispersing billiards
Sep 19, 05
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Abstract. This work is devoted to 2D dispersing billiards with smooth
boundary, i.e. periodic Lorentz gases (with and without horizon).
We revisit several fundamental properties of these systems and
make a number of improvements. The necessity of such improvements
became obvious during our recent studies of gases of several
particles. We prove here that local (stable and unstable)
manifolds, as well as singularity curves, have uniformly
bounded derivatives of all orders. We establish sharp
estimates on the size of local manifolds, on distortion
bounds, and on the Jacobian of the holonomy map.