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Hausdorff Dimension and Conformal Dynamics II: Geometrically Finite Rational Maps
(Birkhäuser Basel, 2000)
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 ...
Winning Sets, Quasiconformal Maps and Diophantine Approximation
(Springer, 2010)
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 ...