Escape Orbits for Non-Compact Flat Billiards

Abstract

It is proven that, under some conditions on $f$, the non-compact flat billiard $\Omega =\{(x,y)\in {\mathbb{R}}_0^{+}\times {\mathbb{R}}_0^{+};0\le y\le f(x)\}$ has no orbits going {\em directly} to $+\infty$. The relevance of such sufficient conditions is discussed.

9 pages, LaTeX, 3 postscript figures available at http://www.princeton.edu/~marco/papers/ . Minor changes since previously posted version. Submitted to 'Chaos'

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