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Full List of Works


+ + + + + PAPERS + + + + +

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)) (arXiv:1907.13488)

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.
(arXiv:1808.08335)


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. (Published online: 17 June 2019 (doi))
(arXiv:1803.03130)


The Riemann hypothesis and holomorphic index in complex dynamics
Exp. Math. 27 (2018) pp 37-46.
(Published online: 11 Oct 2016 (doi))
(arXiv:1602.06843)


Quatre applications du lemme de Zalcman `a la dynamique complexe
J. Anal. Math. 124 (2014) pp 309-336.
(arXiv:1401.4086)


On the natural extensions of dynamics with a Siegel or Cremer point
(with C.Cabrera) J. Difference Equ. Appl. 21 (2013) pp 701-711.
(arXiv:1103.2905v1[math.DS], DOI:10.1080/10236198.2012.681780)


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.

Topology of the regular part for infinitely renormalizable quadratic polynomials
(with C. Cabrera) Fund. Math. 208 (2009) pp 35-56.
(arXiv:math.DS/0706.4225)


Tessellation and Lyubich-Minsky laminations associated with quadratic maps II:
Topological structures of 3-laminations

Conformal Geom. Dyn. 13 (2009) pp 6-75.
(arXiv:math.DS/0609836)


Tessellation and Lyubich-Minsky laminations associated with quadratic maps I:
Pinching semiconjugacies

Ergodic Theory Dynam. Systems 29(2009) no 2. pp 579-612.
(arXiv:math.DS/0609280)


A proof of simultaneous linearization with a polylog estimate
Bull. Polish Acad. Sci. Math. 55(2007), pp 43-52.
(arXiv:math.DS/0609165)


Tessellation and Lyubich-Minsky laminations associated with rabbits.
Preprint, 2005. (Old version of "Tessellation and ...I and II" above)

Semiconjugacies between the Julia sets of geometrically finite rational maps II.
Dynamics on the Riemann Sphere: A Bodil Branner Festschrift, 2006, pp 131 - 138.

Laminations associated with parabolic quadratic polynomials.
Preprint, 2003.(Older version of "Tessellation and ..." above)

On the regular leaf space of the cauliflower.
Kodai Math. J. , 26(2003) pp.167 - 178

Making the Hausdorff measure into an invariant measure on the Julia set.
Preprint, 2001

Semiconjugacies between the Julia sets of geometrically finite rational maps.
Ergodic Theory Dynam. Systems, 23(2003) pp.1125 - 1152.

On dynamical stability of the Julia sets of parabolic rational maps.
Preprint, 2000.


+ + + + + PROCEEDINGS + + + + +

Some new applications of Zalcman's lemma to complex dynamics.
(In Japanese). RIMS Kokyuroku, 1699(2010), pp. 44 - 61.

Rigidity of Riemann surface laminations associated with infinitely renormalizable quadratic maps.
RIMS Kokyuroku, 1586(2008), pp. 160 - 168.

Twisting operations in Lyubich-Minsky laminations associated with bifurcations of quadratic maps.
RIMS Kokyuroku, 1571(2007), pp. 155 - 171.

Simultaneous linearization and its application.
RIMS Kokyuroku, 1537(2007), pp. 143 - 149.

Note on dynamically stable perturbations of parabolics.
RIMS Kokyuroku, 1447(2005), pp 90 - 107.

On perturbation of rational maps and construction of semiconjugacies on the Julia sets.
RIMS Kokyuroku, 1220(2001) pp.121 - 140.

Julia集合にまつわる種々の連続性
(In Japanese). RIMS Kokyuroku, 1087(1999) pp.67 - 92.


+ + + + + BOOK, THESIS, etc. + + + + +

入門 複素関数
裳華房, 2019.

[鼎談] 大学数学の学び方……川平友規+小畑久美+竹山美宏
数学セミナー2016年4月号,日本評論社, 2016.

[鼎談] 大学数学の学び方……川平友規×小畑久美×竹山美宏
数学ガイダンス2016,数学セミナー編集部 編, 日本評論社, 2016.

微分積分 -- 1変数と2変数
日本評論社, 2015.

微分積分は何のためにあるか
数学セミナー2015年6月号,日本評論社, 2015.

基礎講座 複素関数
数学セミナー2014年4月号〜2015年3月号,日本評論社, 2014-2015.

複素数の話
数学セミナー2013年9月号,日本評論社, 2013.

レクチャーズ オン Mathematica
プレアデス出版, 2013.

Riemann's Zeta function, Newton's method and holomorphic index
Poster presentation, 2008. ( old version.)

Semiconjugacies in complex dynamics with parabolic cycles.
Thesis, University of Tokyo, 2003.

Julia集合の放物的分岐に伴う連続性
(In Japanese). Master's Thesis, University of Tokyo, 2000.

Hausdorff次元に関するSullivanの辞書
(with M. Taniguchi, in Japanese). Topics in Complex Analysis 1999.

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