SPEAKER: George Savvidy (Demokritos National Research Centre & INPP, Athens, Greece)
TITLE: Maximally Chaotic Dynamical Systems of Kolmogorov-Anosov and
Fundamental Interactions
ABSTRACT: The interest in maximally chaotic dynamical systems is associated with
the attempts to understand the relaxation phenomena, the foundation of
the statistical mechanics, the appearance of turbulence in fluid
dynamics, the non-linear dynamics of the Yang–Mills field, as well as
the dynamical properties of gravitating N-body systems and the Black
hole thermodynamics. In this respect of special interest are
Anosov–Kolmogorov C-K systems that are defined on Riemannian manifolds
of negative sectional curvature and on a high-dimensional tori. Here we
shall review the classical- and quantum-mechanical properties of
maximally chaotic dynamical systems, the application of the C-K theory
to the investigation of the Yang–Mills dynamics and gravitational
systems, as well as their application in the Monte Carlo method. The
maximally chaotic K-systems are dynamical systems that have nonzero
Kolmogorov entropy. On the other hand, the hyperbolic dynamical systems
that fulfil the Anosov C-condition have exponential instability of their
phase trajectories, mixing of all orders, countable Lebesgue spectrum
and positive Kolmogorov entropy. The C-condition defines a rich class of
maximally chaotic systems that span an open set in the space of all
dynamical systems.
LOCATION: Aula Grassano, Department of Physics, Tor Vergata University
DATE: Monday 14 Oct 2024, 14:00–15:00 CET
