Mathematical method to investigate the rule of the complex phenomena
Department of Mathematics, Mathematics
Study of statistical properties arising from complex systems exhibiting nonhyperbolic phenomena
|Field||Ergodic Theory, Dynamical System, Complex System|
|Keyword||Celestial 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.