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TY - CHAP
TI - The Decomposition Theorem
A2 - Schwartz, Richard Evan
AB - The Room Lemma confines one period of$\Gamma (p/q)$to a certain parallelogram$R(p/q)$when$(p/q)$is odd. In this section we explain a sharper result, along the same lines, that confines one period of$\Gamma (p/q)$to a union of two parallelograms. The reader might want to glance at Figure 19.1 before reading the definitions that follow.

Given an odd rational$A = (p/q)$, we construct the even rationals${A_ \pm } = {p_ \pm }/{q_ \pm }$. We let${A'}$be the inferior predecessor of*A*, and we let$A{\kern 1pt} *$be the superior predecessor, as in §4.1. For each rational, we use Equation 3.2 to construct the corresponding*V*and

EP - 180
PB - Princeton University Press
PY - 2009
SN - 9780691142494
SP - 171
T2 - Outer Billiards on Kites (AM-171)
UR - http://www.jstor.org/stable/j.ctt7t77g.22
Y2 - 2020/11/29/
ER -