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Area and Hausdorff Dimension of Julia Sets of Entire Functions
(American Mathematical Society, 1987)
We show the Julia set of \(\lambda\sin(z)\) has positive area and the action of \(\lambda\sin(z)\) on its Julia set is not ergodic; the Julia set of \(\lambda\exp(z)\) has Hausdorff dimension two but in the presence of ...
Families of Rational Maps and Iterative Root-Finding Algorithms
(Princeton University, 1987)
In this paper we develop a rigidity theorem for algebraic families of rational maps and apply it to the study of iterative root-finding algorithms. We answer a question of Smale's by showing there is no generally convergent ...
A rigorous examination of the Chandrasekhar theory of stellar collapse
(IOP Publishing, 1987)