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Nakano Lab
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The lab reads what happens over long periods of time through the statistics of chaos.
AboutAbout the lab
What lies beyond a long span of time
Prof. Nakano studies dynamical systems theory and ergodic theory.
Dynamical systems theory is a field that examines how a system behaves after a long time has passed, given the law of its evolution over one unit of time.
The objects of study are not limited to mechanical models, but also include mathematical models of natural and social phenomena such as population, stock prices, and rainfall.
The property by which a small change in the initial state later has a large effect is called chaos, and the lab studies the statistical properties of such systems.
Key terms
- Dynamical system
- A mathematical object defined by a rule for how a state changes over time
- Chaos
- The property by which a very small initial difference grows into a large difference over time
- Ergodic theory
- A theory that studies the relationship between the average over a long time and the average over the whole space
ResearchResearch themes
The lab studies dynamical systems theory, which examines how a system with a given law of evolution per unit time behaves after a long time has passed. Chaos makes it difficult to predict the future of an individual orbit, but statistically, its very irregularity makes the system easier to analyze.
*Illustrative imageChaos and statistical properties
In many dynamical systems, such as weather models, a small change in the initial state has a large effect after a long time. This is chaos. Predicting individual orbits becomes difficult, but statistically, the irregularity actually makes analysis easier.
*Illustrative imageNon-hyperbolic dynamical systems
For hyperbolic dynamical systems, which have good differential-geometric properties, statistical properties such as the law of large numbers, the central limit theorem, and the existence and uniqueness of equilibrium measures are known. The lab specializes in non-hyperbolic dynamical systems, which lack these properties, and deals with partially hyperbolic systems with a neutral direction, infinite ergodic chaos arising from neutral fixed points, and systems with homoclinic tangencies.
*Illustrative imageRandom dynamical systems and other variants of dynamical systems
The lab is also interested in variants of dynamical systems, such as random dynamical systems and coupled map systems, which arose from the needs of other natural sciences. It investigates how these differ from conventional dynamical systems.
MembersFaculty
- Associate ProfessorYushi Nakano
VoicesStudent voices
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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: “Hurricane Isabel from ISS” Image courtesy of Mike Trenchard, Earth Sciences & Image Analysis Laboratory, NASA Johnson Space Center. / Public domain (cropped)
- Chaos and statistical properties: “8 scale fractal” Akarpe / CC BY-SA 4.0 (cropped)
- Non-hyperbolic dynamical systems: “Incense smoke against a black sky - Flickr - Vanessa Pike-Russell” Vanessa Pike-Russell from Cleveland, QLD, Australia / CC BY 2.0 (cropped)
- Random dynamical systems and other variants of dynamical systems: “And The Kitchen Sink Too ( )” Jan Bambach / CC BY-SA 3.0 (cropped)
- Related lab (Analysis (Kubo) Lab): “Surface waves” Roger McLassus / CC BY-SA 3.0 (cropped)
- Related lab (Mathematical Sciences (Masaki) Lab): “Baltic Sea Wave (Cien Water)” Marek Nowocień / CC BY 2.5 (cropped)
- Related lab (Honda Lab): “Essential singularity” Functor Salad / CC BY-SA 3.0 (cropped)
- Related lab (Analysis Lab (Yuhei Suzuki)): “AnimSun 13” PrzemekMajewski / CC BY-SA 4.0 (cropped)
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