The exponential map is chaotic: An invitation to transcendental dynamics
  We present an elementary and conceptual proof that the complex exponential map is "chaotic" when considered as a dynamical system on the complex plane. (This result was conjectured by Fatou in 1926 and first proved by Misiurewicz 55 years later.) The only background required is a first undergraduate course in complex analysis. 
Zhaiming Shen and Lasse Rempe-Gillen
math.DS math.CV