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41.
Jean Coste 《Journal of statistical physics》1980,23(4):521-536
We consider a transformation of the unit interval which exhibits a stable periodic attractor and whose topological entropy is positive. We show that the dynamics leading to this attractor has a statistical character. 相似文献
42.
Generalized dimensions,entropies, and Liapunov exponents from the pressure function for strange sets
For conformal mixing repellers such as Julia sets and nonlinear one-dimensional Cantor sets, we connect the pressure of a smooth transformation on the repeller with its generalized dimensions, entropies, and Liapunov exponents computed with respect to a set of equilibrium Gibbs measures. This allows us to compute the pressure by means of simple numerical algorithms. Our results are then extended to axiom-A attractors and to a nonhyperbolic invariant set of the line. In this last case, we show that a first-order phase transition appears in the pressure. 相似文献
43.
A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynamical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force. 相似文献
44.
Pullback exponential attractors for nonautonomous dynamical system in space of higher regularity 下载免费PDF全文
Yongjun Li Tinggang Zhao Hongqing Wu Jinying Wei 《Journal of Applied Analysis & Computation》2016,6(1):242-253
Under what condition, a process which exists a $(E,E)$-pullback exponential attractor implies the existence of $(E,V)$- pullback exponential attractor when $V$ embedded in $E$? We answer this question in this paper. As an application of this result, we prove the existence of pullback exponential attractor for a nonlinear reaction-diffusion equation with a polynomial growth nonlinearity in $L^q(\Omega)(\forall q\geq 2)$ and $H_0^1(\Omega)$. 相似文献
45.
Alexandre N. Carvalho José A. Langa James C. Robinson 《Journal of Differential Equations》2010,249(12):3099-3109
We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. 相似文献
46.
A.Kh. Khanmamedov 《Journal of Differential Equations》2006,225(2):528-548
In this paper, we study the asymptotic behavior of solutions for the plate equation with a localized damping and a critical exponent. We prove the existence, regularity and finite dimensionality of a global attractor in . 相似文献
47.
In this paper we show the existence of the uniform attractors for the family of processes corresponding to the suspension bridge equations in H02 × L2 by a new concept of Condition (C*) and the enegy estimats methods. 相似文献
48.
Zhouchao Wei 《Applied mathematics and computation》2010,217(1):422-429
In order to further understand a complex 3D dynamical system showing strange chaotic attractors with two stable node-foci near Hopf bifurcation point, we propose nonlinear control scheme to the system and the controlled system, depending on five parameters, can exhibit codimension one, two, and three Hopf bifurcations in a much larger parameter regain. The control strategy used keeps the equilibrium structure of the chaotic system and can be applied to degenerate Hopf bifurcation at the desired location with preferred stability. 相似文献
49.
The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied. 相似文献
50.
This article studies the global well-posedness and long-time dynamics for the nonlinear complex Ginzburg–Landau equation involving fractional Laplacian. The global existence and some uniqueness criterion of weak solutions are given with compactness method. To study the strong solutions with the semigroup method, we generalize some pointwise estimates for the fractional Laplacian to the complex background and study carefully the linear evolution of the equation. Finally, the existence of global attractors is studied. 相似文献