Related papers: Spectral theory of dynamical systems
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
This is a review article on the distributions of entry and return times in dynamical systems which discusses recent results for systems of positive entropy.
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
In this article we survey some of the recent developments in the structure theory of set addition.
Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is…
The goal of this paper is to show that there exists a simple, yet universal statistical logic of spectral graph analysis by recasting it into a nonparametric function estimation problem. The prescribed viewpoint appears to be good enough to…
We describe a multispeckle dynamic light scattering technique capable of resolving the motion of scattering sites in cases that this motion changes systematically with time. The method is based on the visibility of the speckle pattern…
For Encyclopedia of Complexist and System Science No abstract given I. Definition and Introduction II. Ising Model III. Fractals IV. Diffusion on Fractals V. Ising Model on Fractals VI. Other Subjects ? VII. Networks VIII. Future Directions
This chapter provides an overview of the different techniques and methods that exist for the analysis and visualization of dynamic networks. Basic definitions and formal notations are discussed and important references are cited. A major…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
We show that dimensional theoretical properties of dynamical systems can considerably change because of number theoretical peculiarities of some parameter values
Vibrational spectroscopy is a powerful technique to characterize the near-equilibrium dynamics of molecules in the gas- and the condensed-phase. This contribution summarizes efforts from computer-based methods to gain insight into the…
This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete…
In this survey of the spectral properties of substitution dynamical systems we consider primitive aperiodic substitutions and associated dynamical systems: ${\mathbb Z}$-actions and ${\mathbb R}$-actions, the latter viewed as tiling flows.…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
Presented here is the mathematical model describing the phenomenon of shock waves. The underlying concept is based on the time-space model of wave propagation.
This is an introductory article to the theory of multiple gaps.
Methods and techniques of the theory of nonlinear dynamical systems and patterns can be useful in astrophysical applications. Some works on the subjects of dynamical astronomy, stellar pulsation and variability, as well as spatial…