Related papers: Chaos in Partial Differential Equations
The occurrence of chaos for test particles moving around a slowly rotating black hole with a dipolar halo is studied using Poincar\'e sections. We find a novel effect, particles with angular momentum opposite to the black hole rotation have…
We present classes of discrete reversible systems which are at the same time chaotic and solvable.
Quantum Chaos has originally emerged as the field which studies how the properties of classical chaotic systems arise in their quantum counterparts. The growing interest in quantum many-body systems, with no obvious classical meaning has…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed description of the spatiotemporally disordered…
I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more…
We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…
We discuss the role of ergodicity and chaos for the validity of statistical laws. In particular we explore the basic aspects of chaotic systems (with emphasis on the finite-resolution) on systems composed of a huge number of particles.
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
Cross section fluctuations in nuclear scattering are briefly reviewed in order to show the main important features. Then chaotic scattering is introduced by means of a very simple model. It is shown that chaoticity produces the same kind of…
The onset of chaos in one-dimensional spinning particle models derived from pseudoclassical mechanical hamiltonians with a bosonic Duffing potential is examined. Using the Melnikov method, we indicate the presence of homoclinic…
A review of chiral perturbation theory and that of recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
This paper is a personal overview of the efforts over the last half century to understand fluid turbulence in terms of simpler coherent units. The consequences of chaos and the concept of coherence are first reviewed, using examples from…
This paper examines the most probable route to chaos in high-dimensional dynamical systems in a very general computational setting. The most probable route to chaos in high-dimensional, discrete-time maps is observed to be a sequence of…
As an enhanced version of existing results on Kac's propagation of chaos, which describes the convergence of mean-field particle systems to a system of independent McKean-Vlasov particles as the number of particles tends to infinity, we…
This review-style article presents an overview of recent progress in constructing and studying critical Gaussian multiplicative chaos. A proof that the critical measure in any dimension can be obtained as a limit of subcritical measures is…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
We prove the existence of fractal solutions to a class of linear ordinary differential equations.This reveals the possibility of chaos in the very short time limit of the evolution even of a linear one dimensional dynamical system.
The astrophysical relevance of chaos for a test particle with spin moving in Schwarzschild spacetime was the objective of \cite{Verhaaren10}. Even if the results of the study seem to be qualitatively in agreement with similar works, the…