id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
7m01bk1495q	Douglas R. Smith	A Method for Estimating Entropy of Real Birational Maps with Constrained Critical Orbits	1904		.txt	text/plain	156	7	56	We particularly concern ourselves with the specific family of maps $f:\overline{\R} \ imes \overline{\R} \ ightarrow \overline{\R} \ imes \overline{\R}$ defined by $f(x,y) = \left(y\ rac{x+a}{x-1},x+a-1\ ight)$, where $a \in \R$ is a parameter subject to conditions specified later. Our method is combinatorial, using invariant and critical curves for $f$ to define a partition of $\overline{\R} \ imes \overline{\R}$ that is convenient for coding orbits under $f$. We may expand these codings to hold for points without well-defined orbits.	cache/7m01bk1495q.txt	txt/7m01bk1495q.txt