INOU Hiroyuki

Japanese

SNS, Web services

• Twitter (@HiroyukiInou)
  • Movies and pictures on VR, 4D, 3D etc. (tweets are in Japanese)
• GitHub
• Shadertoy
  

Programming

• QFract: a Qt-based fractal viewer (Last update: 9 Jan 2023.)
• HHKPS2USBDriver for Snow Leopard Slightly edited the original driver by NAKAhashi Ichiro for Snow Leopard.
• Beamer blackboard color theme (Distributed under LPPL.)

3D/4D visualizations

• See the web page of MACS VR Study Group (in Japanese).
• Double spherical (3D) pendulum (WebVR, 6.5MB)
• 2D & 3D pendulums (WebVR, 5.9MB)
• 3D self-similar sets (WebGL, 4.6MB)
• Julia sets on the Riemann sphere (WebGL, 39MB) Recommended browser: Chrome (at least Firefox on my Mac crashes!)

3D and 4D objects

• The zero locus of the Green's function on C² for one-dimensional complex dynamics

Pictures

• Pictures for (near-)parabolic renormalizations

Movies

• Polyvision: 4D Space Manipulation through Multiple Projections.
  
  (See also the publication.)
• MACS SG2 (2018) report (youtube, 360° movie)
  
• The internal ray of angle 0 in the adjacent component of the cubic periodic curve of period 2 (similar to spinning deformation by Pilgrim-Tan). avi (58M)

Workshops

• RIMS Symposium "Complex dynamics and related topics" (2025)
• RIMS Symposium "Recent progress in complex dynamics and related topics" (2024/12)
• IMI Workshop "Interactive cognition of higher dimension with VR 2" (2022/8)
• IMI Workshop "Interactive cognition of higher dimension with VR" (2021/2)

Publications, preprints

• Straightening Maps for Polynomials with One Bounded Critical Orbit. J. Geom. Anal. 33, 314 (2023) (with Y. Wang).
• Accessible hyperbolic components in anti-holomorphic dynamics. arXiv:2203.12156.
• Discontinuity of straightening in anti-holomorphic dynamics: I. Trans. Amer. Math. Soc. (with S. Mukherjee).
• Discontinuity of straightening in antiholomorphic dynamics: II. Int. Math. Res. Not., Volume 2022, Issue 9 (2022), 6948-6990 (with S. Mukherjee).
• Polyvision: 4D Space Manipulation through Multiple Projections. SIGGRAPH Asia 2019 Emerging Technologies (with K. Matsumoto, N, Ogawa, S. Kaji, Y. Ishii and M. Hirose). (See above for the movie)
• Double Pendulum.
• On The Support of The Bifurcation Measure of Cubic Polynomials. Math. Ann. 378 (2020), 1-12 (with S. Mukherjee). Movie
• Self-similarity for the tricorn. Exp. Math. 28 (2019) 440-455.
• An implosion arising from saddle connection in 2D complex dynamics. Indiana Univ. Math. J. 68 (2019), 35-61. (with S. Nakane).
• Non-landing parameter rays of the multicorns. Invent. Math. 204 (2016) 869-893 (with S. Mukherjee).
• Visualization of the bifurcation locus of cubic polynomial family.
• Combinatorics and topology of straightening maps II: Discontinuity, arXiv:0903.4289.
• Extending local analytic conjugacies. Trans. AMS. 363 (2011), 331-343. (former title: Analytic conjugacy classes of polynomial-like mappings).
• Combinatorics and topology of straightening maps I: compactness and bijectivity. Adv. Math. 231 (2012), 2666-2733 (with Jan Kiwi). (Preprint version in arXiv). r
• The renormalization for parabolic fixed points and their perturbation, submitted (with Mitsuhiro Shishikura).
• Limits of renormalizable polynomials. Nonlinearity 19 (2006), 1769--1799.
• Homeomorphisms from Julia sets into connectedness loci. Ergodic Theory & Dynamical Systems (2006), 26, 1087--1113.
• Renormalization and rigidity of polynomials of higher degree. J. Math. Kyoto Univ. 42 (2002), no. 2, 351--392.
• Surgery construction for inverse branches of renormalization operator (PDF)

Talks

• An example of an infinitely renormalizable cubic polynomial and its combinatorial class. Holomorphic dynamics and related fields, Shanghai Center for Mathematical Sciences (September 26, 2019).
• Discontinuity of straightening maps. Aspects of Transcendental Dynamics, Jacobs University, Bremen (June 20, 2008).

SheepShaver screenshots (running on a FreeBSD machine)

• FractalAsm on SheepShaver

  

• SaddleDrop on SheepShaver

  

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Inou Hiroyuki <inou at math dot kyoto-u dot ac dot jp>