Web page of Zin ARAI

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Research Interest

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Chubu University Academy of Emerging Sciences
email: zin●isc.chubu.ac.j

Research Interest

I have been studying dynamical systems using topological and computational methods. My particular interest lies in the real and complex Hénon maps, especially in the structure of their parameter spaces. I am also working on the application of topological and computational methods to several areas, including chemistry, engineering, and biology.

Keywords: Conley index, Computational Topology, Hyperbolic Dynamics, Validated Numerics, Computer Assisted Proofs, Monodromy, Hénon map, etc.


Research Papers

Proceedings and survey articles


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.



Programs for rigorous verification 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 ad-hoc 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.


link to iruka hotel

GAIO memo (Japanese)
A Japanese introduction of GAIO.
Iruka Hotel
I'm the drummer of Iruka Hotel, a three-piece rock band formed in Kyoto.