Related papers: Spectral theory of dynamical systems
Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time…
We give an overview of the status of string cosmology. We explain the motivation for the subject, outline the main problems, and assess some of the proposed solutions. Our focus is on those aspects of cosmology that benefit from the…
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical Spin Noise…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to…
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
In this contribution we establish a dictionary between terms in two different areas in order to show that many of the topics studied are common ones - just with a different terminology. We further analyze the relations between the…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
I review various theory issues in diffraction that have been presented and discussed in the working group on diffractive interactions, and a few points concerning the comparison of theory with data.
Another way to evaluate the spectral-correlation properties of thermal fields of solids is suggested. Such a method takes into account detailed structure of the interface transition layer separating one bulk region from those of the vacuum…
Some spectral data analysis methods that are useful for the two-dimensional imaging diagnostics data are introduced. It is shown that the frequency spectrum, the local dispersion relation, the flow shear, and the nonlinear energy transfer…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
In the framework of the approximation of slowly varying amplitudes a multiwave dynamical theory of neutron diffraction on a moving phase grating was developed. The influence of the velocity of the grating, its period and height of the slits…
The theory of causal fermion systems is an approach to describe fundamental physics. We here introduce the mathematical framework and give an overview of the objectives and current results.