http://www.cam.cornell.edu/Graduate/Courses/#dynamical"
http://www.math.umd.edu/research/dynamics/"
http://www.math.psu.edu/dynsys/"
http://www.math.sunysb.edu/dynamics/"
I am an applied math major, so those are all math programs. I'm strongly considering going into dynamics as well. I have taken PDEs, ODEs, classical dynamics, and have signed up for my first official "dynamical systems" class next semester. This is a pretty common route.
Many physicists study non-linear dynamics as well, for what it's worth. Both of my classical dynamics books contain entire chapters on chaos.
Not enough info for ya? http://www.dynamicalsystems.org/ap/pg/"