Related papers: Semiflows on finite topological spaces

We present new experimental results on the development of turbulent spots in channel flow. The internal structure of a turbulent spot is measured, with Time Resolved Stereoscopic Particle Image Velocimetry. We report the observation of…

We study $2$-dimensional unit vector flows on graphs, that is, nowhere-zero flows that assign to each oriented edge a unit vector in $\mathbb R^{3}$. We give a new geometric characterization of $\mathbb S^{2}$-flows on cubic graphs. We also…

In this paper we analyze some applications of the category of exterior spaces to the study of dynamical systems (flows). We study the notion of an absorbing open subset of a dynamical system; i.e., an open subset that contains the "future…

In this paper we analyze the long-time behaviour of 3 dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric…

We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow,…

We prove that for any complete three-manifold with a lower Ricci curvature bound and a lower bound on the volume of balls of radius one, a solution to the Ricci flow exists for short time. Actually our proof also yields a (non-canonical)…

These lecture notes aim to present some of the ideas behind the recent (conditional) existence and (weak-strong) uniqueness theory for mean curvature flow. Focusing on the simplest case of the evolution of a single closed hypersurface…

Constructions of metrics with special holonomy by methods of exterior differential systems are reviewed and the interpretations of these construction as `flows' on hypersurface geometries are considered. It is shown that these hypersurface…

It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier-Stokes equations if the viscosity $\nu$ is small enough, provided the horizontal wave number $\alpha$ lies in a small interval,…

A topology on a nonempty set $X$ specifies a natural subset of $\mathcal{P}(X)$. By identifying $\mathcal{P}(\mathcal{P}(X))$ with the totally disconnected compact Hausdorff space $2^{\mathcal{P}(X)}$, the lattice $Top(X)$ of all topologies…

We investigate the emergence of finite-amplitude non-zonal flows on the sphere $\mathbb{S}^2$ arising from stationary solutions to the 2D Euler equations. By restricting the Laplace-Beltrami eigenspace to the invariant subspace of the…

In this paper, we study inextensible flows of non-null curves in E^n,1. We give necessary and sufficient conditions for inextensible flow of nonnull curves in E^n,1.

This paper gives a topological characterization of Hamiltonian flows with finitely many singular points on compact surfaces, using the concept of ``demi-caract\'eristique'' in the sense of Poincar\'e. Furthermore, we describe the…

We consider bifurcation of solutions from a given trivial branch for a class of strongly indefinite elliptic systems via the spectral flow. Our main results establish bifurcation invariants that can be obtained from the coefficients of the…

We provide an example of Cherry flow (i.e. smooth flow on the $2$-dimensional torus with a sink and a saddle) having quasi-minimal set which is an attractor. The first return map for such a flow, constructed also in the paper, is a smooth…

The topological dynamics of the horocyclic flow h_R on the unit tangent bundle of a geometrically finite hyperbolic surface is well known. In particular on such a surface the flow h_R is minimal or the minimal sets are the periodic orbits.…

In this paper we study the dynamics of Bernoulli flows and their subflows over general countable groups from the symbolic and topological perspectives. We study free subflows (subflows in which every point has trivial stabilizer), minimal…

We study {\sf traversing} vector flows $v$ on smooth compact manifolds $X$ with boundary. For a given compact manifold $\hat X$, equipped with a traversing vector field $\hat v$ which is {\sf convex} with respect to $\partial\hat X$, we…

We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…

In cylindrical domain, we consider the nonstationary flow with prescribed inflow and outflow, modelled with Navier-Stokes equations under the slip boundary conditions. Using smallness of some derivatives of inflow function, external force…