MPEJ Volume 12, No. 1, 54 pp.
Received: Aug 29, 2005. Revised: Nov 30, 2005. Accepted:  Jan 6, 2006.

N. Chernov
Regularity of local manifolds in dispersing billiards

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.

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http://www.ma.utexas.edu/mpej/Vol/12/1.ps
http://www.ma.utexas.edu/mpej/Vol/12/1.pdf

http://mpej.unige.ch/mpej/Vol/12/1.ps
http://mpej.unige.ch/mpej/Vol/12/1.pdf