# Bounded contraction, hyperbolicity, and J-stability in non-archimedean dynamics

ALGEBRAIC DYNAMICS

##### Speaker:

Robert Benedetto *- Amherst College*

Let K be a complete and algebraically closed field, such as C or the p-adic field C_p, and let f\in K(z) be a rational function of degree d\geq 2. The map f is said to be hyperbolic if there is some metric on its Julia set with respect to which it is expanding. A celebrated 1983 theorem of Mane, Sad, and Sullivan shows that for K=C, hyperbolic maps are J-stable, meaning that nearby maps in moduli space have topologically conjugate dynamics on their Julia sets. In this talk, we show that if K is non-archimedean, an a priori weaker bounded-contraction condition also yields J-stability. This project is joint work with Junghun Lee.

Go to http://people.math.harvard.