526 citations
- Gemini North ObservatoryUS3 papers
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math.DS2009
Rational Misiurewicz maps for which the Julia set is not the whole sphere
Magnus Aspenberg
We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.
math.DS2009
The dual nest for degenerate Yoccoz puzzles
Magnus Aspenberg
The Yoccoz puzzle is a fundamental tool in Holomorphic Dynamics. The original combinatorial argument by Yoccoz, based on the Branner-Hubbard tableau, counts the preimages of a non-…
math.DS2007★ 1 cited
Rational Misiurewicz maps are rare
Magnus Aspenberg
We show that the set of Misiurewicz maps has Lebesgue measure zero in the parameter space of rational maps for any fixed degree greater than or equal to 2.
math.DS2004
Recurrence of entire transcendental functions with simple post singular sets
Jan-Martin Hemke
We study how the orbits of the singularities of the inverse of a meromorphic function prescribe the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We c…