Researcher Information

Michiko Yuri

Professor

Mathematical method to investigate the rule of the complex phenomena

Department of Mathematics, Mathematics

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Theme

Study of statistical properties arising from complex systems exhibiting nonhyperbolic phenomena

FieldErgodic Theory, Dynamical System, Complex System
KeywordCelestial mechanics, Chaos, Dissipative system, Intermittency, Multifractal, Nonhyperbolic system, Phase transition, Statistical mechanics, Symbolic dynamics

Introduction of Research

The purpose of our project is to present mathematical ideas and methods which are useful in predicting asymptotic behavior of complex systems.
In particular, we are interested in dynamics of complex systems exhibiting "nonhyperbolic" phenomena and in applying our results to a number of the applied sciences, (e.g., in neuroscience, physics, chemistry and economics).
Our techniques are based on ergodic theory arising from equilibrium statistical physics.
We develop a new concept that may be adapted to nonequilibrium steady states exhibiting dissipative phenomena producing non-stationary processes.
This allows us to study statistical properties of complex systems admitting both chaotic and fractal structures.