Tomoki Kawahira

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Name
Tomoki Kawahira
Affiliation
Tokyo Institute of Technology
Section
School of Science
Job title
Associate Professor
Research funding number
50377975

Research Areas

 
 

Published Papers

 
Yi-Chiuan Chen, Tomoki Kawahira
Journal of Mathematical Analysis and Applications   473 345-356   May 2019   [Refereed]
For the complex quadratic family Tex, it is known that every
point in the Julia set Tex moves holomorphically on Tex except at the
boundary points of the Mandelbrot set. In this note, we present short proofs of
the following ...
Yi-Chiuan Chen, Tomoki Kawahira
Trans. Amer. Math. Soc.      Jun 2019   [Refereed]
For the quadratic family Tex with Tex in the exterior of the
Mandelbrot set, it is known that every point in the Julia set moves
holomorphically. Let Tex be a semi-hyperbolic parameter in the boundary
of the Mandelbrot set. In...
Kawahira Tomoki
Experimental Mathematics   27(1) 37-46   2018   [Refereed]
Tomoki Kawahira
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...
Carlos Cabrera, Tomoki Kawahira
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 Tex with irrational Tex 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
C.Cabrera and Tomoki Kawahira
Fund. Math.   208 35-56   Jan 2010   [Refereed]
Tomoki Kawahira
Conform. Geom. Dyn. 13 (2009) pp 6-75      Sep 2006   [Refereed]
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...
Tomoki Kawahira
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...
Tomoki Kawahira
Bull. Polish Acad. Sci. Math. 55 (2007) pp 43-52      Sep 2006   [Refereed]
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]
On the regular leaf space of the cauliflower
Tomoki Kawahira
Kodai Math. J. ,   26 167-178   2003   [Refereed]
Semiconjugacies between the Julia sets of geometrically finite rational maps
Tomoki Kawahira
Ergodic Theory & Dynamical Systems   23 1125 - 1152.   2003   [Refereed]

Misc

 
Tomoki Kawahira
   Jul 2019
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...
Tomoki Kawahira, Masashi Kisaka
   Mar 2018
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
Tomoki Kawahira
数理解析研究所講究録   1220 128-140   2001   [Invited]