This paper investigates several dynamically defined dimensions for rational maps \(f\) on the Riemann sphere, providing a systematic treatment modeled on the theory for Kleinian groups. We begin by defining the radial Julia ...

This paper describes two new types of winning sets in \(\mathbb{R}^n\), defined using variants of Schmidt’s game. These strong and absolute winning sets include many Diophantine sets of measure zero and first category, and ...