Abstract:

By studying the recurrence governing the sequence of degrees of birational mappings, we get the following result:

Proposition Consider the parametric family of birational mappings [f(x,y)=(ax,frac{c+x}{d+y}).] Then, $f$ is globally periodic if and only if there exists a $pin mathbb{N}$ such that $f^p(-ac,0)=(-c,-d).$ In this case $f$ is $2p+2$-periodic. 

This is a joint work with Sundus Zafar.