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Hayashi Lab
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A lab that uses mathematics to study how systems change over time.
AboutAbout the lab
The big picture of dynamical systems, through ergodic theory
The Hayashi Lab studies differentiable dynamical systems on manifolds, in the fields of dynamical systems and ergodic theory.
The lab is working on a conjecture asking whether dynamical systems that exhibit homoclinic bifurcations, together with hyperbolic dynamical systems, are dense in the space of all dynamical systems.
To this end, the lab has brought in the perspective of ergodic theory and has tried to build hyperbolicity from invariant measures.
Key terms
- Dynamical system
- A mathematical description of how the state of a system changes over time
- Hyperbolicity
- A property of dynamical systems in which orbits contract in some directions and expand in others
- Homoclinic bifurcation
- A phenomenon in which an orbit leaving a point returns to that same point, changing the behavior of the dynamical system
ResearchResearch themes
The lab's research fields are dynamical systems and ergodic theory. It studies generic properties of differentiable dynamical systems on manifolds, as well as hyperbolicity and homoclinic bifurcations.
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MembersFaculty
- Associate ProfessorShuhei HayashiPublications ↗
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Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Hayashi Lab
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Shiraishi LabFaculty of Science, Department of MathematicsMathematical PhysicsThe information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
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: “Lorenz attractor and its transients” Yapparina / CC0 (cropped)
- Generic Properties of Differentiable Dynamical Systems and Hyperbolicity: “Smale Horseshoe Map” SyntaxError55 at English Wikipedia / CC BY-SA 3.0 (cropped)
- Related lab (Willox Lab): “Two soliton overtake collision - color plot” N0fk / CC BY-SA 4.0 (cropped)
- Related lab (Kato Lab): “Orange Genus 2 Surface” Gelada / CC BY-SA 3.0 (cropped)
- Related lab (Matsui Lab): “Illustration of Yang Baxter Equation” AHusain314 / Public domain (cropped)
- Related lab (Shiraishi Lab): “Weierstrass p function” Claudio Rocchini / CC BY-SA 4.0 (cropped)
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