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Arai Lab
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A lab that unravels dynamical systems with the power of topology and computers.
AboutAbout the lab
Building a bridge between pure mathematics and concrete problems
Arai Lab studies the mathematics of dynamical systems and computational topology.
The lab aims to use computer science to build a bridge between pure mathematics and concrete problems.
It is particularly interested in real and complex Hénon maps and the structure of their parameter spaces.
The lab is also pursuing research that applies topological and computational methods to fields such as chemistry, engineering, and biology.
Key terms
- Dynamical systems
- A mathematical framework that treats phenomena changing over time in terms of rules describing how a state changes
- Computational topology
- A method of using computers to investigate rough properties of shapes, such as how their parts are connected and whether they have holes
- Verified numerical computation
- A way of computing that includes the range of error in the result and shows that the answer certainly lies within that range
ResearchResearch themes
The lab studies dynamical systems using topological and computational methods. It is interested in real and complex Hénon maps and the structure of their parameter spaces, and its research keywords include the Conley index, computational topology, hyperbolic dynamical systems, verified numerical computation, and computer-assisted proofs.
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MembersFaculty
- ProfessorZin AraiPublications ↗
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Poisson saturne revisited” Bvsydow / CC BY-SA 4.0 (cropped)
- Understanding the Behavior of Hénon Maps: “Fractal of henon attractor” Yapparina / CC0 (cropped)
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- Related lab (安永憲司研究室): “ENIGMA Wired Rotor - National Cryptologic Museum - DSC07768” Daderot / CC0 (cropped)
- Related lab (田中健一郎研究室): “Domain coloring x2-1 x-2-i x-2-i d x2+2+3i” Djiboun / CC BY-SA 4.0 (cropped)
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