[02023] Theory and applications of random/no-autonomous dynamical systems part IV
Session Time & Room : 2C (Aug.22, 13:20-15:00) @F309
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 IV, we discuss anomalous statistics and non-stationarity in random dynamical systems.
[05589] Physical applications of infinite ergodic theory
Format : Talk at Waseda University
Author(s) :
Eli Barkai (Bar Ilan University)
Abstract : We show how non-normalised Boltzmann Gibbs measure can still yield statistical averages and thermodynamic properties of physical observables, exploiting a model of Langevin dynamics of a single Brownian
particle in an asymptotically flat potential. Similar tools are applicable for a gas of sub-recoiled laser cooled
atoms and weakly chaotic non-linear oscillators.
[03122] Transition to Anomalous Dynamics in A Simple Random Map
Format : Talk at Waseda University
Author(s) :
Jin Yan (Max Planck Institute for the Physics of Complex Systems)
Moitrish Majumdar (International Centre for Theoretical Sciences - TIFR)
Stefano Ruffo (SISSA Trieste)
Yuzuru Sato (Hokkaido University)
Christian Beck (Queen Mary University of London)
Rainer Klages (Queen Mary University of London)
Abstract : A random dynamical system consists of a setting where different types of dynamics are sampled randomly in time. Here we consider a simple yet universal example, where an expanding or a contracting map is randomly selected at each discrete-time with probability $p$ or $1-p$, respectively. By continuously varying $p$ between zero and one, we found anomalous behaviour characterised by an infinite non-normalisable invariant density, weak ergodicity breaking, and a power-law decay in correlations.
[05573] Arcsine law for random dynamics with a core
Format : Talk at Waseda University
Author(s) :
Yushi Nakano (Tokai University)
Fumihiko Nakamura (Kitami Institute of Technology)
Hisayoshi Toyokawa (Kitami Institute of Technology)
Kouji Yano (Osaka University)
Abstract : The arcsine law is a characterization of intermittent dynamics in infinite ergodic theory. A well-known model of intermittent dynamics is an interval with two increasing surjective branches being uniformly expanding except for indifferent fixed points at the boundary. We show that the arcsine law holds for random dynamics with a core, which is a class of random iterations of two interval maps without indifferent periodic points but "indifferent in average" at the boundary.
[05570] Infinite ergodic theory in physics
Format : Talk at Waseda University
Author(s) :
Takuma Akimoto (Tokyo University of Science)
Abstract : Infinite ergodic theory provides a distributional behavior of time-averaged observables in dynamical systems. We show that the infinite ergodic theory plays an important role in physics. In particular, we show several distributional limit theorems for time-averaged observables in non-stationary stochastic processes that are models of anomalous diffusion and laser-cooled systems.
