.png){kind=icon}
.png){kind=icon}
Return
Billiards in regular polygons
.png){kind=icon}
PRE
AI
DOI：10.4171/lem/1099.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper we study billiards in regular n-sided polygons and monodromy over Teichm & uuml;ller curves from an arithmetic perspective. Our main results show that the combinatorics of billiards in a periodic direction s is controlled by the projection of s to a finite projective line.This arithmetic control coexists, experimentally, with chaotic behavior that first emerges when n=12.
Keywords:
Billiards
Teichm & uuml
ller theory
cyclotomic fields
thin groups