Graduate Student Colloquium
Hexi Ye
UIC
Rational Functions with Identical Measure of Maximal Entropy
Abstract: Let $f$ be a generic rational function with degree $d \geq 3$. We
are going to show that for any rational function $g$ with $\mu_f=\mu_g$
(the same measure of maximal entropy), $f$ and $g$ have some common
iterate--i.e., $f^n=g^m$. Moreover, we are going to give non-exceptional functions $f$
and $g$, with the same degree and measure, such that there is no $\sigma$ in
$PSL_2(\mathbb{C})$ and no $n \geq 1$ with $f^n=\sigma \circ g^n$ (which cannot happen in the polynomial case).
This talk is meant to be accessible for graduate students of all levels; no technical knowledge of complex dynamics is expected.
Monday March 5, 2012 at 4:15 PM in SEO 636