Syracuse Maps as Non-singular Power-Bounded Transformations and Their Inverse Maps

Idris Assani, Ethan Ebbighausen, Anand Hande

We prove that the dynamical system $(\mathbb{N},2^{\mathbb{N}},T,\mu )$, where $\mu$ is a finite measure equivalent to the counting measure, is power-bounded in $L^1(\mu )$ if and only…