Chaotic differentiation operators on harmonic functions and simple connectivity

Cyclic behavior of holomorphic functions on a Runge region

“…Shapiro [20] later showed that if D is the differentiation operator and P is a nonconstant polynomial then P ( D ) : H (Ω) → H (Ω) is hypercyclic if and only if Ω ⊂ C is simply connected. A harmonic version of Shapiro's result was obtained by Chan, Kadel, and 2 Pinheiro [8].…”