Add to ORKGAbstract: A semigroup of continuous operators in a Hilbert space is considered. It is shown that the fractal dimension of a compact strictly invariant set admits the same estimate as the Hausdorff dimension, namely, both are bounded from above by the Lyapunov dimension calculated in terms of the global Lyapunov exponents. Applications of the results so obtained to the two-dimensional Navier-Stokes equations are given.Note: Research direction:Mathematical problems and theory of numerical method
International audienceWe consider a family of Leray- models with periodic boundary conditions in thr...
We consider finite energy solutions for the damped and driven two-dimensional Navier--Stokes equatio...
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal di...
Abstract. A semigroup St of continuous operators in a Hilbert space H is considered. It is shown tha...
In recent years many deterministic parabolic equations have been shown to possess global attractors ...
We study the fractal and Hausforff dimensions of the universal attractor for the Navier-Stokes equat...
In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact ...
In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact ...
Abstract. In this paper we present two approaches to estimate the Hausdorff dimension of an invarian...
AbstractIn recent years many deterministic parabolic equations have been shown to possess global att...
Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semi...
Abstract. Herein I define the global attractor for the semidynamical system (H, {S(t)}t≥0), where H ...
We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Sigma(m) ={0, ... ...
For conservative dynamical systems, the invariant sets which are in a sense the analog of the strang...
This paper is dedicated to estimate the fractal dimension of exponential global attractors of some g...
International audienceWe consider a family of Leray- models with periodic boundary conditions in thr...
We consider finite energy solutions for the damped and driven two-dimensional Navier--Stokes equatio...
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal di...
Abstract. A semigroup St of continuous operators in a Hilbert space H is considered. It is shown tha...
In recent years many deterministic parabolic equations have been shown to possess global attractors ...
We study the fractal and Hausforff dimensions of the universal attractor for the Navier-Stokes equat...
In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact ...
In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact ...
Abstract. In this paper we present two approaches to estimate the Hausdorff dimension of an invarian...
AbstractIn recent years many deterministic parabolic equations have been shown to possess global att...
Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semi...
Abstract. Herein I define the global attractor for the semidynamical system (H, {S(t)}t≥0), where H ...
We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Sigma(m) ={0, ... ...
For conservative dynamical systems, the invariant sets which are in a sense the analog of the strang...
This paper is dedicated to estimate the fractal dimension of exponential global attractors of some g...
International audienceWe consider a family of Leray- models with periodic boundary conditions in thr...
We consider finite energy solutions for the damped and driven two-dimensional Navier--Stokes equatio...
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal di...