YURI, Michiko

YURI, Michiko
Research Field
Applied Mathematics
Department of Mathematics
Research Interest
Ergodic Theory, Dynamical System, Complex System
Research Activities

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.

(1) M.Yuri. Statistical properties for nonhyperbolic maps with finite range structure.
Trans. AMS, 352 (2000), 2369-2388

(2) M.Yuri. Thermodynamic Formalism for countable to one Markov systems.
Trans. Amer. Math. Soc. 355 (2003), 2949-2971

(3) M.Yuri. Entropy production at weak Gibbs measures and a generalized
variational principle. Ergodic Theory and Dynamical Systems 29 (2009), 1327-1347

Book :
[1] M.Pollicott & M.Yuri. Dynamical Systems and Ergodic Theory.
Cambridge University Press. (1998)

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