Journal of Mathematical Analysis and Applications 473 345-356 May 2019 [Refereed]
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 Mandelbrot set. In this note, we present short proofs of
the following ...
For the quadratic family with in the exterior of the
Mandelbrot set, it is known that every point in the Julia set moves
holomorphically. Let be a semi-hyperbolic parameter in the boundary
of the Mandelbrot set. In...
J. d'Analyse Math. 124 309-336 Jan 2014 [Refereed]
We give four applications of Zalcman's lemma to the dynamics of rational maps
on the Riemann sphere: a parameter analogue of a proof of the density of
repelling cycles in the Julia sets;similarity between the Mandelbrot set and
the Julia sets; a c...
J. Difference Equ. Appl. 21 (2013) pp 701-711 Mar 2013 [Refereed]
In this note we show that the regular part of the natural extension (in the
sense of Lyubich and Minsky) of quadratic map with irrational of bounded type has only parabolic leaves except
the invariant li...
Family of invariant cantor sets as orbits of differential equations, II: Julia sets
Y-C Chen, T. Kawahira, H-L Li, and J-M Yuan
Inter. J. Bifur. & Chaos 21(2011) 77-99 Jan 2011 [Refereed]
Topology of the regular part for infinitely renormalizable quadratic polynomials
According to an analogy to quasi-Fuchsian groups, we investigate topological
and combinatorial structures of Lyubich and Minsky's affine and hyperbolic
3-laminations associated with the hyperbolic and parabolic quadratic maps.
We begin by showin...
Ergodic Theory Dynam. Systems 29 (2009) pp 579-612 Sep 2006 [Refereed]
We introduce tessellation of the filled Julia sets for hyperbolic and
parabolic quadratic maps. Then the dynamics inside their Julia sets are
organized by tiles which work like external rays outside. We also construct
continuous families of pinchi...
We give an alternative proof of simultaneous linearization recently shown by
T.Ueda, which connects the Schröder equation and the Abel equation
analytically. Indeed, we generalize Ueda's original result so that we may apply
it to the parabolic f...
Semiconjugacies between the Julia sets of geometrically finite rational maps II.
Tomoki Kawahira
Dynamics on the Riemann Sphere (A Bodil Branner Festschrift) 131-138 2006 [Refereed]
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 phenomenon in terms of Zalcman functions, that is, entire
functions gen...
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 image of a Cantor Julia set which is a perturbation of
a parabolic or ...
Some new applications of Zalcman's lemma to complex dynamics
Tomoki Kawahira
1699 44-61 2010 [Invited]
Rigidity of Riemann surface laminations associated with infinitely renormalizable quadratic maps
Tomoki Kawahira
1586 160-168 2008 [Invited]
Simultaneous linearization and its application
Tomoki Kawahira
数理解析研究所講究録 1537 143-149 2007 [Invited]
Twisting operations in Lyubich-Minsky laminations associated with bifurcations of quadratic maps
Tomoki Kawahira
1571 155-171 2007 [Invited]
Note on dynamically stable perturbations of parabolics
Tomoki Kawahira
数理解析研究所講究録 1447 90-107 2005 [Invited]
On perturbations of rational maps and construction of semiconjugacies on the Julia sets
