[02023] Theory and applications of random/no-autonomous dynamical systems part IV

Session Date & Time : 2C (Aug.22, 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 IV, we discuss anomalous statistics and non-stationarity in random dynamical systems.

Jin Yan (Max Planck Institute for the Physics of Complex Systems)

Takuma Akimoto (Tokyo University of Science)

Yushi Nakano (Tokai University)

Talks in Minisymposium :

[03122] Transition to Anomalous Dynamics in A Simple Random Map

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.