You seem to be convinced use the fact that the set of points and directions where $L(\epsilon)=\infty$ has measure zero. Since one One can translate this problem to considering closed billiard paths through $p$ in a square, which avoid the corners by $\epsilon$ I wonder if \epsilon$. In the vicinity of a closed path this is truemay be used to bound the number of reflections necessary to reach a corner.
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You seem to be convinced that the set of points and directions where $L(\epsilon)=\infty$ has measure zero. Since one can translate this problem to considering closed billiard paths through $p$ in a square, which avoid the corners by $\epsilon$ I wonder if this is true. |
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