23 citations · 56 across the 5 of their papers we have counts for
4 papers · 1 filter
Wandering domains for entire functions of finite order in the Eremenko-Lyubich class
David Martí-Pete, Mitsuhiro Shishikura
Recently Bishop constructed the first example of a bounded-type transcendental entire function with a wandering domain using a new technique called quasiconfomal folding. It is eas…
The high type quadratic Siegel disks are Jordan domains
Mitsuhiro Shishikura, Fei Yang
Let be an irrational number of sufficiently high type and suppose has a Siegel disk centered at the origin. We prove that the boundary of is…
Satellite renormalization of quadratic polynomials
Davoud Cheraghi, Mitsuhiro Shishikura
We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on an infinite-dimensional space of holomorphic transformations. This implies the universa…
The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
Mitsuhiro Shishikura
It is shown that the boundary of the Mandelbrot set has Hausdorff dimension two and that for a generic $c \in \bM$, the Julia set of also has Hausdorff dimens…