Related papers: Spectral theory of dynamical systems
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
This is a survey of the spectral theory of tensors.
A stochastic dynamics framework for the study of complex systems is presented.
Expanded lecture notes. Preliminary version, comments are welcome.
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.
This is a slightly modified version of the survey article. Minor changes to the text and the references have been made.
This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such…
The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…
We present here the concept of Dominated Splitting and give an account of some important results on its dynamics.
Thermodynamical aspects of string theory are reviewed and discussed.
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
The scope of the paper is a theoretical analysis of the dynamical system, the model of which was reduced to Weierstrasse function. A fractal structure of the trajectory was proved and the entropy of the system information designated.
We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more…
This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection…
The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
We study the Hamiltonian dynamics and spectral theory of spin-oscillators. Because of their rich structure, spin-oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have…
Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as…
We use molecular dynamics simulations to compute the Lyapunov spectra of many-particle systems resembling simple fluids in thermal equilibrium and in non-equilibrium stationary states. Here we review some of the most interesting results and…