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 ...

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 ...