Related papers: Solvable Chaos
A multiparameter class of integrable systems is introduced.
The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this…
Even as we understand for long that the world is quantal and buried in it is classical dynamics which is chaotic, finding eigenfunctions analytically from the the Schroedinger equation has turned out to be a near-impossibility. Here, we…
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts…
We consider a singularly perturbed fourth-order problem with third-order terms on the unit square. With a formal power series approach, we decompose the solution into solutions of reduced (third-order) problems and various layer parts. The…
The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values…
This communication records some observations made in the course of studying one-relator groups from the point of view of residual solvability. As a contribution to clas- sification efforts we single out some relator types that render the…
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…
We give a method to determine an explicit solution to a system of two inhomogeneous linear recursive sequences of higher order. Our approach can be used efficiently in solving certain combinatorial problems. We finish the paper by…
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…
Variable order differential equations with non-integrable singularities are considered on spatial networks. Properties of the spectrum are established, and the solution of the inverse spectral problem is obtained.
We discuss stationary solutions of the nonlinear Schrodinger equation (NSE) applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or…
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…
The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fr\'{e}chet space. The other is about…
We consider the classical response in a chaotic system. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in a chaotic system vanishes at long times. The response also reveals certain…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible…
As well-known, the concept "hypercyclic" in operator theory is the same as the concept "transitive" in dynamical system. Now the class of hypercyclic operators is well studied. Following the idea of research in hypercyclic operators, we…
Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…