Infinite genus surfaces and irrational polygonal billiards

Details Infinite genus surfaces and irrational polygonal billiards Infinite genus surfaces and irrational polygonal billiards

2008-11-05

arxiv.org/abs/0811.0728v2

Mathematics

Dynamical Systems

15 pages, 18 figures

Scientific paper

We prove that the natural invariant surface associated with the billiard game
on an irrational polygonal table is homeomorphic to the Loch Ness monster, that
is, the only orientable infinite genus topological real surface with exactly
one end.

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