Related papers: Fixed points, bounded orbits and attractors of pla…
In this paper the notion of global attractor is extended from the setting of semigroup actions on metric spaces to the setting of semigroup actions on uniformizable spaces. General conditions for the existence of global attractor are…
We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof,…
We discuss various issues related to the finite-dimensionality of the asymptotic dynamics of solutions of parabolic equations. In particular, we study the regularity of the vector field on the global attractor associated with these…
Spinor fields which are covariantly constant with respect to a connection with flux are of particular interest in unified string theories and supergravity theories, as their existence is required by supersymmetry. In this paper, flows of…
Toric differential inclusions occur as key dynamical systems in the context of the Global Attractor Conjecture. We introduce the notions of minimal invariant regions and minimal globally attracting regions for toric differential inclusions.…
The sensitivity of many physics analyses can be enhanced by constructing discriminants that preferentially select signal events. Such discriminants become much more useful if they are uncorrelated with a set of protected attributes. In this…
We show that the stochastic flow generated by the Stochastic Navier-Stokes equations in a 2-dimensional Poincar\'e domain has a unique random attractor. This result complements a recent result by Brze\'zniak and Li [10] who showed that the…
We give a detailed study of attractors for measure driven quintic damped wave equations with periodic boundary conditions. This includes uniform energy-to-Strichartz estimates, the existence of uniform attractors in a weak or strong…
We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard equation…
Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we…
Given an integer m>1 we consider Zm-equivariant and orientation preserving homeomorphisms in the plane with an asymptotically stable fixed point at the origin. We present examples without periodic points and having some complicated…
This paper deals with global asymptotic stability of prolongations of flows induced by specific vector fields and their prolongations. The method used is based on various estimates of the flows.
We compare various concepts of attractor in the context of non-autonomous dynamical systems. Then, we prove an appropriate version of the Pliss reduction principle for non-autonomous differential systems with rapidly oscillating…
We consider the characterization of global attractors $A_f$ for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form $u_t = u_{xx} + f(u,u_x)$, defined on the circle $x\in S^1$, for a class of reversible…
This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H.…
In [Adv. Math., 267(2014), 277-306], Cheskidov and Lu develop a new framework of the evolutionary system that deals directly with the notion of a uniform global attractor due to Haraux, and by which a trajectory attractor is able to be…
We discuss the non-equilibrium attractors of systems undergoing Gubser flow within kinetic theory by means of nonlinear dynamical systems. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR)…
The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make…
An open question in the study of dilation surfaces is to determine the typical dynamical behavior of the directional flow on a fixed dilation surface. We show that on any one-holed dilation torus, in all but a measure zero Cantor set of…
It is a paper about models for isolated sets and the construction of special hyperbolic Lyapunov functions. We prove that after a suitable surgery every isolated set is the intersection of an attractor and a repeller. We give linear models…