迭代函数系统的吸引子的维数估计

某些迭代函数系统（ＩＦＳ）的吸引子的Ｈａｕｓｄｏｒｆ维数的经典估计通常由求解两个非线性方程的解得到．在相同条件下，本文给出了一些显式不等式估计，使经典估计是其中的特殊情形．而且某些ＩＦＳ的吸引子的维数可以通过求解满足一定条件的非线性方程而得出     

The Global Attractors for the Periodic Initial Value Problem of Generalized Kuramoto-Sivashinsky Type Equations in Multi-dimensions

The existence of global attractors for the periodic initial value problem of generalized Kuramoto-Sivashinsky type equations in multi-dimensions is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniform priori estimates for time.     

The Global Attractors for Damped Generalized Coupled Nonlinear Wave Equations

The existence of global attractors for the periodic initial value problem of damped generalized coupled nonlinear wave equations is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniformly priori estimates for time.     

Finite Dimensional Behavior for Weakly Damped Generalized KdV-Burgers Equations

ＦｉｎｉｔｅＤｉｍｅｎｓｉｏｎａｌＢｅｈａｖｉｏｒｆｏｒＷｅａｋｌｙＤａｍｐｅｄＧｅｎｅｒａｌｉｚｅｄＫｄＶ－Ｂｕｒｇｅｒｓ　ＥｑｕａｔｉｏｎｓＧｕｏＢｏｌｉｎｇ（郭柏灵）（ＣｅｎｔｒｅｆｏｒＮｏｎｌｉｎｅａｒＳｔｕｄｉｅｓ，ＩｎｓｔｉｔｕｔｅｏｆＡ...     

The Global Attractors for the Periodic Initial Value Problem For a Coupled Non-linear Wave Equation

The existence of global attractors of the periodic initial value problem for a coupled non-linear wave equation is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of uniform a priori estimates for time.     

耗散的广义对称正则长波方程周期初值问题的整体吸引子

该文考虑了带有耗散项的广义对称正则长波方程解的长时间性态.证明了周期初值问题整体吸引子的存在性,用关于时间的一致先验估计获得整体吸引子的Hausdorff和分形维数的上界估计.     

The Global Attractors for the Dissipative Generalized Hasegawa-Mima Equation

The long time behavior of solutions of the generalized Hasegawa-Mima equation with dissipation term is considered. The existence of global attractors of the periodic initial value problem is proved, and the estimate of the upper bound of the Hausdorff and fractal dimensions for the global attractors is obtained by means of uniform a priori estimates method.     

Global attractors for the initial value problems of Cohn-Hilliard equations on compact manifolds

In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems we prove the existence of global attractors for the initial value problem of Cahn-Hilliard equations. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are also obtained.     

Attractors and Dimensions for Discretizations of a Dissipative Zakharov Equations

Abstract In this paper, a dissipative Zakharov equations are discretized by difference method.We make priorestimates for the algebric system of equations. It is proved that for each mesh size,there exist attractors forthe discretized system.The bounds of the Hausdorff dimensions of the discrete attractors are obtained,and thevarious bounds are dependent of the mesh sizes.     

Global Solutions and Their Large-time Behavior of Cauchy Problem for Equations of Deep Water Type

We consider the large time behavior of the global solution of the Cauchy problem for the equation of Benjamin-Ono type. A series of large-time global estimates for Cauchy problem arc constructed. By means of the obtained global estimates uniformly for 0 ≤ t < ∞, the attractors of the Cauchy problem for the mentioned nonlinear equations are considered. And also the dimensions of the global attractor are estimated.     

带五次项的NLS方程及其谱逼近的整体吸引子的维数估计

通过给出一般发展方程和其近似方程解的整体吸引子的Hausdorff维数上界间的关系，继[1，2]的讨论，本文进一步得到了带五次项的NLS方程和半离散Fourier谱近似解的整体吸引子的Hausdorff维数的上界估计。     

Bounds for attractors and the existence of homoclinic orbits in the lorenz system

Frequency estimates are derived for the Lyapunov dimension of attractors of non-linear dynamical systems. A theorem on the localization of global attractors is proved for the Lorenz system. This theorem is applied to obtain upper bounds for the Lyapunov dimension of attractors and to prove the existence of homoclinic orbits in the Lorenz system.     

Attractors and Dimensions for Discretizations of a NLS Equation with a Non-local Nonlinear Term

In this paper we consider a semi-dicretized nonlinear Schrödinger (NLS) equation with local integral nonlinearity. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds for the Hausdorff and fractal dimensions of the discrete attractors are obtained, and the various bounds are independent of the mesh sizes. Furthermore, numerical experiments are given and many interesting phenomena are observed such as limit cycles, chaotic attractors and a so-called crisis of the chaotic attractors.     

Long time behavior for damped generalized coupled nonlinear wave equations.Ⅰ.Bounded domain

Introduction In [1], the authors established the unique ekistence of the smooth solution for the couplednonlinear equations. These were proposed to describe the iateraction process of internal longwaves. In [2], Ito proposed a recursion operator by which he inferred that the equations possess infinitely many symmetries and constants of motion. In [3], He established the ealstenceo f a smooth solution to the system of coupled nonlinear KdV equationl41. We remark thatSchonbekls] dealt' with a…     

ATTRACTORS FOR DISCRETIZATION OF GINZBURG-LANDAU-BBM EQUATIONS

1. IntroductionIn this paper) we consider the following periodic initial value problem for the system ofGinzburg-Landau equation coupled with BBM equationwhere e(x,t) is a complex function, n(x, t) is a real scalar function, at a, 5, 7, al, a2, FI, adZare real constants, and gi (x), g200 are given real functions.This problem describes the nonlinear interactions between Langmuir wave and ion acousticwave in plasma physics, e(x, t) denotes electric field, n(x, t) the perturbation of density (…     

Global attractor for the nonlinear strain waves in elastic waveguides

1. IntroductionIn some problems of nonlinear wave propagation in waveguides, the illteraction of waveguides and the external medium and, therefore, the possibility of energy exchange throughlateral surface of waveguide cannot be neglected. When the energy exchange between therod and the medium is considered, for one cajse, there is a dissipation of deformation wavein the viscous external medium. The general cubic double dispersion equation (CDDE) canbe derived from Hamilton principled]:where…     

Lyapunov Functions in Dimension Estimates of Attractors of Dynamical Systems

We discuss relations between the Lyapunov dimension and the topological, Hausdorff, and fractal dimensions of attractors. For the Henon and Lorenz systems, explicit formulas characterizing the Lyapunov dimension of their attractors are obtained. Bibliography: 23 titles.     

An exact formula for the measure dimensions associated with a class of piecewise linear maps

An exact formula for the various measure dimensions of attractors associated with contracting similitudes is given. An example is constructed showing that for more general affine maps the various measure dimensions are not always equal.Communicated by Michael F. Barnsley.     

具阻尼的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计

本文得到了一类具有线性阻尼且非线性项满足临界增长条件的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计．     

Exploiting geometric signatures to accurately determine properties of attractors

We explore the notion of the geometric signature and demonstrate that it could be utilized in order to estimate dimensions, characterize lacunarity and type of attractor (self-similar, nonself-similar), and determine the length of transients for attractors.