Papers / Preprints
Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof
(with M.Kisaka) Preprint (Submitted).
From hyperbolic to parabolic parameters along internal rays
(with Y.-C. Chen) Trans. Amer. Math. Soc. 377 (2024) (Published electrically on 15 May 2024) (doi)
Accessible hyperbolic components in anti-holomorphic dynamics
(with H. Inou) Preprint (arXiv:2203.12156)
Zalcman functions and similarity between the Mandelbrot set, Julia sets, and the tricorn
Anal. Math. Phys. 10, Article number: 16 (2020). (In the special issue "Perspectives in Modern Analysis". (doi))
Simple proofs for the derivative estimates of the holomorphic motion near two boundary points of the Mandelbrot set
(with Y.-C. Chen) J. Math. Anal. App. 473 (2019) pp 345-356.
Julia sets appear quasiconformally in the Mandelbrot set
(with M. Kisaka) Preprint (arXiv:1804.00176)
From Cantor to semi-hyperbolic parameter along external rays
(with Y.-C. Chen) Trans. Amer. Math. Soc. 372 (2019) pp 7959-7992. (doi)
The Riemann hypothesis and holomorphic index in complex dynamics
Exp. Math. 27 (2018) pp 37-46. (Published online: 11 Oct 2016 (doi))
Quatre applications du lemme de Zalcman `a la dynamique complexe.
J. d'Analyse Math. 124 (2014) pp 309-336.
On the natural extensions of dynamics with a Siegel or Cremer point
(with C.Cabrera) J. Difference Equ. Appl. 21 (2013) pp 701-711.
Family of invariant Cantor sets as orbits of differential equations, II: Julia sets
(with Y.-C. Chen, H.-L. Li, and J.-M. Yuan) Inter. J. Bifur. & Chaos. 21 (2011) pp 77-99. (doi))
Topology of the regular part for infinitely renormalizable quadratic polynomials
(with C. Cabrera) Fund. Math. 208 (2010) pp 35-56.
Tessellation and Lyubich-Minsky laminations associated with quadratic maps, II: Topological structures of 3-laminations
Conform. Geom. Dyn. 13 (2009) pp 6-75.
Tessellation and Lyubich-Minsky laminations associated with quadratic maps, I: Pinching semiconjugacies
Ergodic Theory Dynam. Systems 29 (2009) pp 579-612.
A proof of simultaneous linearization with a polylog estimate
Bull. Polish Acad. Sci. Math. 55 (2007) pp 43-52.
Semiconjugacies between the Julia sets of geometrically finite rational maps II
in Dynamics on the Riemann Sphere: A Bodil Branner Festschrift, Eur. Math. Soc., 2006, pp 131-138.
On the regular leaf space of the cauliflower
Kodai Math. J. 26 (2003) pp.167 - 178.
Semiconjugacies between the Julia sets of geometrically finite rational maps
Ergodic Theory Dynam. Systems 23 (2003) pp.1125 - 1152.
Full List of Works
Miscellaneous
Notes on Tan's theorem on similarity between the Mandelbrot set and the Julia sets
not for publication, 2013. (Now included in this paper.) 		An algorithm to draw external rays of the Mandelbrot set
not for publication, 2009. (Now included in this paper.)
Notes on dynamically stable perturbations of parabolics
RIMS Kokyuroku 1447 (2005), pp 90 - 107. 		Some new applications of Zalcman's lemma to complex dynamics
(In Japanese) RIMS Kokyuroku 1699 (2010), pp 44 - 61.
Semiconjugacies in complex dynamics with parabolic cycles.
Thesis, University of Tokyo, 03/2003. 		Hausdorff次元に関するSullivanの辞書
(with M. Taniguchi, in Japanese). Topics in Complex Analysis 1999.
Slides
Topology of the Lyubich-Minsky laminations for quadratic maps: Deformation and rigidity
(1st | 2nd | 3rd) Jussieu, Paris, 12/2008. 		複素力学系におけるラミネーション理論：変形と剛性
 (In Japanese) Nagoya，Japan, 12/2009.
Zalcmanの補題と複素力学系
 (In Japanese) Kyoto, Japan, 03/2013. (印刷用)
( → 講演アブストラクト) 		タイヒミュラー空間の基礎のキソ
 (In Japanese) Toba, Japan, 08/2012. (印刷用)
Books
入門　複素関数
裳華房，2019年2月刊． 		Full-List
微分積分 -- 1変数と2変数
 日評ベーシック・シリーズ，日本評論社，2015年7月刊． 		レクチャーズ オン Mathematica
 2013年5月刊行．プレアデス出版．