5 citations · 23 across the 14 of their papers we have counts for
14 papers
Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof
Tomoki Kawahira, Masashi Kisaka
Following the ideas of A.~Douady, we give an alternative proof of the authors' result: for any boundary point of the Mandelbrot set , we can find small quasiconformal copi…
From Hyperbolic to Parabolic Parameters along Internal Rays
Yi-Chiuan Chen, Tomoki Kawahira
For the quadratic family with in a hyperbolic component of the Mandelbrot set, it is known that every point in the Julia set moves holomorphically. In this p…
Accessible hyperbolic components in anti-holomorphic dynamics
Hiroyuki Inou, Tomoki Kawahira
The tricorn, the connectedness locus of the anti-holomorphic quadratic family, is known to be non-locally connected. The boundary of every hyperbolic component of odd period contai…
Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn
Tomoki Kawahira
We present a simple proof of Tan's theorem on asymptotic similarity between the Mandelbrot set and Julia sets at Misiurewicz parameters. Then we give a new perspective on this phen…
Simple Proofs for the Derivative Estimates of the Holomorphic Motion near Two Boundary Points of the Mandelbrot Set
Yi-Chiuan Chen, Tomoki Kawahira
For the complex quadratic family , it is known that every point in the Julia set moves holomorphically on except at the boundary points of the Mand…
Julia sets appear quasiconformally in the Mandelbrot set
Tomoki Kawahira, Masashi Kisaka
In this paper we prove the following: Take any "small Mandelbrot set" and zoom in a neighborhood of a parabolic or Misiurewicz parameter in it, then we can see a quasiconformal ima…