相关论文: Finite Fractal Dimension of uniform attractors for…
The aim of this paper is to propose a new method to construct exponential attractors for infinite dimensional dynamical systems in Banach spaces with explicit fractal dimension. The approach is established by combing the squeezing…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
The existence of a pullback attractor is established for the singularly perturbed FitzHugh-Nagumo system defined on the entire space $R^n$ when external terms are unbounded in a phase space. The pullback asymptotic compactness of the system…
The aim of this paper is to study the finite-dimensional approximations of the nonautonomous lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z)\ (*)$. We show that the…
In this paper we propose a new model of random graph directed fractals that extends the current well-known model of random graph directed iterated function systems, $V$-variable attractors, and fractal and Mandelbrot percolation. We study…
A new method is presented to prove finiteness of the fractal and Hausdorff dimensions of the global attractor for the strong solutions to the 3D Primitive Equations with viscosity, which is applicable to even more general situations than…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1…
A method is suggested for the computation of the generalized dimensions of fractal attractors at the period-doubling transition to chaos. The approach is based on an eigenvalue problem formulated in terms of functional equations, with a…
In this paper, we define inhomogeneous Graph-Directed (GD) separation conditions for a given inhomogeneous GD Iterated Function Systems (IFS), and estimate the upper box dimension of attractors by the dimension of the condensation set and…
Under general boundary conditions we consider the finiteness of the Hausdorff and fractal dimensions of the global attractor for the strong solution of the 3D moist primitive equations with viscosity. Firstly, we obtain time-uniform…
In this paper, we apply an implicit Euler scheme to discretize the complex Ginzburg-Landau equation and prove the existence of a numerical attractor for the discrete Ginzburg-Landau system. We establish the upper semicontinuity of the…
Iterated function systems (IFSs) are one of the most important tools for building examples of fractal sets exhibiting some kind of `approximate self-similarity'. Examples include self-similar sets, self-affine sets etc. A beautiful variant…
We consider the dimension and measure of typical attractors of random iterated function systems (RIFSs). We define a RIFS to be a finite set of (deterministic) iterated function systems (IFSs) acting on the same metric space and, for a…
We establish the effective {\em finite dimensionality} of the dynamics corresponding to a flow-plate interaction PDE model arising in aeroelasticity: a nonlinear panel, in the absence of rotational inertia, immersed in an inviscid potential…
The main objective of this paper is to obtain estimations of Hausdorff dimension as well as fractal dimension of global attractors and pullback attractors for both autonomous and nonautonomous functional differential equations (FDEs) in…
We study the fractal dimension of a class of solenoidal attractors in dimensions greater or equal than 3, proving that if the contraction is sufficiently strong, the expansion is close to conformal and the attractor satisfy a geometrical…
Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semiflow generated by the semilinear damped wave equation u_{tt}+\alpha u_t+\beta(x)u-\Deltau = f(x,u), (t,x)\in[0,+\infty[\times\Omega, u = 0,…