Related papers: Turbulent homeomorphisms and the topological snail
The motion of point vortices constitutes an especially simple class of solutions to Euler's equation for two dimensional, inviscid, incompressible, and irrotational fluids. In addition to their intrinsic mathematical importance, these…
Global intermittency is observed in the stably stratified Atmospheric Boundary Layer (ABL) and corresponds to having large nonturbulent flow regions to develop in an otherwise turbulent flow. In this paper, the differences between…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in…
Point-like motile topological defects control the universal dynamics of diverse two-dimensional active nematics ranging from shaken granular rods to cellular monolayers. A comparable understanding in higher dimensions has yet to emerge. We…
The study of the dynamics of a surface homeomorphism in the neighbourhood of an isolated fixed point leads us to the following results. If the fixed point index is greater than 1, a family of attractive and repulsive petals is constructed,…
A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…
The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features.…
This paper generalizes the classical notion of turbulence from dynamical systems generated by continuous functions to those defined by closed relations on compact metric spaces. Using the Mahavier product and the associated shift map, we…
Neutral surfaces, along which most of the mixing in the ocean occurs, are notoriously difficult objects: they do not exist as well-defined surfaces, and as such can only be approximated. In a hypothetical ocean where neutral surfaces are…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
The dynamics and statistical properties of two-dimensional (2D) turbulence are often investigated through numerical simulations of incompressible, viscous fluids in doubly periodic domains. A key challenge in 2D turbulence research is…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
In this paper, we give an introduction for rough groups and rough homomorphisms. Then we present some properties related to topological rough subgroups and rough subsets. We construct the product of topological rough groups and give an…
This article discusses the description of wall-bounded turbulence as a deterministic high-dimensional dynamical system of interacting coherent structures, defined as eddies with enough internal dynamics to behave relatively autonomously…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…
We give a unified proof of the existence of turbulence for some classes of continuous interval maps which include, among other things, maps with periodic points of odd periods > 1, some maps with dense chain recurrent points and densely…
We exhibit a continuously varying family $F_\lambda$ of homeomorphisms of the sphere $S^2$, for which each $F_\lambda$ is a measurable pseudo-Anosov map. Measurable pseudo-Anosov maps are generalizations of Thurston's pseudo-Anosov maps,…
Self-similar curves are a recurring motif in nature. The tension-free stationary states of conformally invariant energies describe the simplest curves of this form. Planar logarithmic spirals, for example, are associated with conformal…
Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…