Lasse Rempe

(University of Liverpool)

Abstract: Transcendental dynamics studies the iteration of functions of one complex variable that have at least one essential singularity (e.g., non-polynomial analytic self-maps of the complex plane, such as exponential or trigonometric functions). That is, for such a map $$f$$ and a complex starting value $$z$$, we consider the long-term behaviour of $$f^n(z)=f\Biggl(f\Big(\ldots\big(f(z)\big)\ldots\Big)\Biggr)$$. While the subject is nearly a century old, it has received increasing attention recently, partly due to intriguing connections with other areas of mathematics.