Related papers: Spectral theory of dynamical systems
We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…
A brief overview is given of recent progress in understanding the dynamics of hot gauge theories.
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
We provide an introduction to mathematical theory of scattering resonances and survey some recent results.
We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down.…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
In this article, we review the mathematical modeling for the vascular system.
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are…
We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…
We present a data model describing the structure of spectrophotometric datasets with spectral and temporal coordinates and associated metadata. This data model may be used to represent spectra, time series data, segments of SED (Spectral…
We characterize the spectrum (and its parts) of operators which can be represented as G=A+BC for a simpler operator A and a structured perturbation BC. The interest in this kind of perturbations is motivated, e.g., by perturbations of the…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.