Papers / Preprints
From hyperbolic to parabolic parameters along internal rays
(with Y.-C. Chen) To appear in Trans. Amer. Math. Soc. (arXiv:2304.11231)
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
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not for publication, 2013.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.
(with M. Taniguchi, in Japanese). Topics in Complex Analysis 1999.
Topology of the Lyubich-Minsky laminations for quadratic maps: Deformation and rigidity
(1st | 2nd | 3rd) Jussieu, Paris, 12/2008.
(In Japanese) Nagoya,Japan, 12/2009.
(In Japanese) Kyoto, Japan, 03/2013. (印刷用)
( → 講演アブストラクト)
(In Japanese) Toba, Japan, 08/2012. (印刷用)
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