Professor
Chubu University
Academy of Emerging Sciences
I have been studying dynamical systems using topological and computational methods.
My current interest is on the real and complex Hénon map, especially on the structure of its hyperbolic horseshoe locus and the monodromy representation of it.
Travel Schedule
Research Papers

Zin Arai, Yutaka Ishii and Hiroki Takahasi,
"Boundary of the horseshoe locus for the Hénon family",
arXiv:1803.09381,
to appear in SIAM Journal on Applied Dynamical Systems.

Takuro Tsutsumi, Yuriko Ono, Zin Arai and Tetsuya Taketsugu,
"A visualization of the intrinsic reaction coordinate and global reaction route map by classical multidimensional scaling", to appear in Journal of Chemical Theory and Computation.

Zin Arai and Yutaka Ishii,
"On parameter loci of the Hénon family",
Communications in Mathematical Physics 361(2), 343414, DOI 10.1007/s0022001831740.
Preprint version: arXiv:1501.01368.

Zin Arai,
"On Loops in the Hyperbolic Locus of the Complex Hénon Map and Their Monodromies",
Physica D 334 (2016), 133140.
PDF of the preprint version,
Supplemental Materials (data, programs).

Zin Arai,
"Decomposition and clustering for the visualization of dynamical systems",
Mathematical Progress in Expressive Image Synthesis I,
Springer (2014), ISBN 9784431550068, 1320.

Zin Arai,
"A rigorous numerical algorithm for computing the linking number of links",
Nonlinear Theory and Its Applications, Vol. 4, No. 1 (2013), 104110,
Supplemental Materials (INTLAB source code).
There is a typo in the published version (thanks to Dr. Simon Copar).
The return value of Algorithm 3 should be doubled. This does not affect the INTLAB code above.
PDF of the corrected version

Zin Arai,
Marcio Gameiro, Tomas Gedeon, Hiroshi Kokubu, Konstantin Mischaikow and Hiroe Oka,
"Graphbased topological approximation of saddlenode bifurcation in maps",
RIMS Kokyuroku Bessatsu
B 31 (2012), 225241.

Zin Arai,
Kazunori Hayashi and Yasuaki Hiraoka,
"MayerVietoris sequences and coverage problems in sensor networks",
Japan Journal of Industrial and Applied Mathematics
28 (2011), 237250.

Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka and P. Pilarczyk,
"A databases schema for the global dynamics of multiparameter systems",
SIAM Journal on Applied Dynamical Systems
8 (2009), 757789.
PDF.

Z. Arai, H. Kokubu and P. Pilarczyk,
"Recent development in rigorous computational methods in dynamical systems",
Japan Journal of Industrial and Applied Mathematics
26 (2009), 393417.
PDF.

Zin Arai,
"On Hyperbolic Plateaus of the Hénon Map",
Experimental Mathematics
16:2 (2007), 181188.
PDF

Zin Arai and Konstantin Mischaikow,
"Rigorous Computations of Homoclinic Tangencies",
SIAM Journal on Applied Dynamical Systems
5 (2006), 280292.
PDF
 Zin Arai,
"Equivalence of Graded Module Braids and Interlocking Sequences",
Journal of Mathematics of Kyoto University
43 (2003), 441449.
PDF
 Zin Arai,
"Tangencies and the Conley Index",
Ergodic Theory and Dynamical Systems
22 (2002), no.4, 973999.
Proceedings and survey articles

Zin Arai, Hiroshi Kokubu and Ippei Obayashi,
"Capturing the global behavior of dynamical systems with ConleyMorse graphs",
Advances in Cognitive Neurodynamics
(III) 2012, Springer, 665672.

Zin Arai,
"Hyperbolicity, stability and monodromy of dynamical systems",
PAMM,
Volume 7 (2007),
Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting.

Zin Arai,
"On applications of computational homology to dynamical systems" (Japanese),
Bul. of Jap. Soc. for Ind. and App. Math. 18 (2008).

Zin Arai,
"On computer assisted analysis of discrete dynamical systems" (Japanese),
Bul. of Jap. Soc. for Ind. and App. Math. 15 (2005),
2031.

Zin Arai,
"On Loops in the Hyperbolic Loci of the Complex Hénon Maps" (Japanese),
RIMS Kokyuroku. PDF (11 pages, 425KB)

Zin Arai,
"On Applications of Rigorous Computing to Dynamical Systems" (Japanese),
RIMS Kokyuroku. PDF (13 pages, 466KB)

Zin Arai,
"The Conley index and transition matrix for discrete dynamical systems and their applications" (Japanese),
A survey article based on my master's thesis.
Includes an introduction for the Conley index theory and the Morse decomposition.
PDF (49 pages, 490KB)
Programs for the Characterization of the maximal entropy locus of complex Hénon Family
Here are
Programs and Data for the rigorous verifications used in "On parameter loci of the Hénon family" by ZA and Yutaka Ishii.
See the
instructions on how to comiple and execute the program. (Last update: Feb 22, 2016, minor bug fixes)
Program for Proving Hyperbolicity of the complex Hénon Map
Here are
Programs and Data for the computation of monodromies associated to loops in the hyperbolic horseshoe locus of the complex Hénon Map.
Program for Proving Hyperbolicity of the real Hénon Map
Here is a program to prove the uniform hyperbolicity of the chain recurrent set of the real Hénon maps.
The algorithm of the program is described in "On Hyperbolic Plateaus of the Hénon Maps".
To run the program you need
MATLAB and
GAIO.
You also need
CAPD if you want to compile the program by yourself.
README
realhenon.tar.gz
Programs for Computation of Tangencies
A program which implements the algorithm given in "Rigorous Computations of Homoclinic Tangencies"
by ZA and Konstantin Mischaikow is available as tangency.tar.gz. See README for the instruction.
Patches for BIAS and Profil on PowerPC G5
To use BIAS and Profil on PowerPC G5 (PowerPC 970),
you have to add some assembler code to the program.
Here is an adhoc patch for BiasInt.h.
Although this patch is for the BIAS package distributed with GAIO,
I think you can easily modify it for other versions of BIAS.
 GAIO memo (Japanese)
 A Japanese introduction of GAIO.
 Iruka Hotel
 I'm the drummer of Iruka Hotel, a threepiece rock band formed in Kyoto.