071 Dan Nicks

Dan Nicks (University of Nottingham) // Iterating the minimum modulus // Abstract: For an entire function f there may or may not exist an r > 0 such that the iterated minimum modulus $m^n(r)$ tends to infinity. Here $m(r) = m(r,f) = \min\{ |f(z)| : |z|=r \}$. Focussing mainly on the class of real transcendental entire functions of finite order with only real zeroes, we discuss some results about the existence of an r > 0 such that $m^n(r) \to \infty$. This is motivated by the result that, for functions in this class, the existence of such an r implies connectedness of the escaping set $\{ z : f^n(z) \to \infty \}$. This is joint work with Phil Rippon and Gwyneth Stallard.