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4 papers · 2 filters
Filled Julia sets with empty interior are computable
I. Binder, M. Braverman, M. Yampolsky
We show that if a polynomial filled Julia set has empty interior, then it is computable.
Hausdorff dimension and conformal measures of Feigenbaum Julia sets
Artur Avila, Mikhail Lyubich
We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon'', there exist many Feigenbaum Julia s…
Weak mixing for interval exchange transformations and translation flows
Artur Avila, Giovanni Forni
We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of ge…
Non-computable Julia sets
Mark Braverman, Michael Yampolsky
We show that under the definition of computability which is natural from the point of view of applications, there exist non-computable quadratic Julia sets.