Symbolic Dynamics Of Billiard Flow In Isosceles Triangles
We provide a complete characterization of billiard trajectory hitting sequences () () on [pi] -isosceles triangles for n [GREATER-THAN OR EQUAL TO] 2. The case of the [pi] -isosceles triangle is pren 4 sented in detail. When n equals two or three, these triangles tile the plane. For n greater than or equal to four, this is no longer the case. On the two isosceles tri() angles that tile the plane, as well as the [pi] -isosceles triangle, we provide combi4 natorial renormalization schemes that apply directly to hitting sequences given in a three letter aphabet of triangle side labels. Although cutting sequences have been characterized on related translation surfaces, this is the first analysis of billiard trajectory hitting sequences in triangles.
symbolic dynamics; polygonal billiards; translation surfaces
Smillie, John D
Earle, Clifford J; Hubbard, John Hamal
Ph. D., Mathematics
Doctor of Philosophy
dissertation or thesis