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[02072] Theory and applications of random/non-autonomous dynamical systems: Part I

  • Session Date & Time : 1C (Aug.21, 13:20-15:00)
  • Type : Proposal of Minisymposium
  • Abstract : Dynamical systems evolving in the existence of noise, is called random dynamical systems. The basic properties, such as stability, bifurcation, and statistical properties, of such random or non-autonomous dynamical systems have not been well studied in mathematics and physics. Recently, cooperative research on random dynamical systems has been developed in the fields in statistical and nonlinear physics, dynamical system theory, ergodic theory, and stochastic process theory. In this mini-symposium, we consider theory and applications of random dynamical systems. In Part I, we discuss computational ergodic theory and applications in random dynamical systems.
  • Organizer(s) : Hiroki Sumi, Yuzuru Sato, Kouji Yano, Takuma Akimoto
  • Classification : 37H05, 37H10, 37H20
  • Speakers Info :
    • Maria Jose Pacifico (UFRJ)
    • Isaia Nisoli (UFRJ)
    • Yuzuru Sato (Hokkaido University)
    • Miki Kobayashi (Rissho University)
  • Talks in Minisymposium :
    • [03478] New characterizations of noise-induced order
      • Author(s) :
        • Yuzuru Sato (Hokkaido University)
      • Abstract : This talk includes a brief review of phenomenologies of non-autonomous / random dynamical systems, followed by a few examples of typical noise-induced phenomena in random dynamical systems. In particular, we present recent results on new characterizations of noise-induced order.
    • [03935] Recent developments on Lorenz-like attractors
      • Author(s) :
        • MARIA JOSE PACIFICO (Federal University of Rio de Janeiro)
      • Abstract : The Lorenz attractor has been playing a central role in the research of singular flows, i.e., flows generated by smooth vector fields with singularities. In this talk I shall survey about old and new results describing the dynamics of this kind of attractors from the topological as well as the ergodic point of view. I will end sketching the proof of my result establishing that in a C1-open and densely family of vector fields (including the classical Lorenz attractor), if the point masses at singularities are not equilibrium states, then there exists a unique equilibrium state supported on Λ. In particular, there exists a unique measure of maximal entropy for the ow X|Λ.
    • [03936] Rigorous enclosure of spectra and its applications
      • Author(s) :
        • Isaia Nisoli (Universidade Federal do Rio de Janeiro)
        • Alex Blumenthal (Georgia Tech)
        • Toby Taylor-Crush (Loughbourugh University)
        • Yuzuru Sato (Hokkaido University)
      • Abstract : In this talk I will introduce a tool developed in collaboration with Dr. A. Blumenthal and Dr. T. Taylor-Crush to rigorously enclose the finite spectrum of a Markov operator. I will then introduce some applications to the study of the phenomenology of important examples of random dynamical systems developed by Prof. Y. Sato.
    • [04094] Time-delayed feedback control for random dynamical systems
      • Author(s) :
        • Miki Kobayashi (Rissho University)
        • Yuzuru Sato (Hokkaido University)
      • Abstract : We propose a framework of Pyragas control for random dynamical systems. The deterministic Pyragus control adopts delayed feedback controls to stabilize a UPO in the original deterministic strange attractor. We demonstrate a few examples including stochastic Rossler dynamics.