具有双曲不变集系统的极限跟踪性

本文证明了Riemann流形上的微分同胚f在其双曲不变集附近具有相对于C1小扰动一致的极限 跟踪性.还证明了如果f是C1-结构稳定的,则,具有极限跟踪性.     

The structure on invariant measures of <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript> generic diffeomorphisms

Let Λ be an isolated non-trivial transitive set of a C 1 generic diffeomorphism f ∈ Diff (M ). We show that the space of invariant measures supported on Λ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ (which implies that the set of irregular+ points is also residual in Λ). As an application, we show that the non-uniform hyperbolicity of irregular+ points in Λ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in Λ) determines the uniform hyperbolicity of Λ.     

平均跟踪与伪轨跟踪

证明了紧致度量空间中有伪轨跟踪的distal同胚不具有平均跟踪性,并给出了有平均跟踪性的同胚是极小的一个充分条件。     

Diffeomorphisms with C 1-stably average shadowing

Let M be a closed smooth manifold M, and let f : M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f . We show that if f has the C1-stably average shadowing property on Λ, then Λ admits a dominated splitting.     

SOME TOPOLOGICAL PROPERTIES OF ENDOMORPHISMS OF THE UNIT CIRCLE

In this paper, we give a simple proof for some topological properties of endomorphisms on the unit circle.     

疯狂动力系统的一些性质

针对纤维映射为旋转的疯狂动力系统,比较系统的研究了它们的回复性、混合性、混沌性等基本的动力学性质.     

Shadowing and Inverse Shadowing for C^1 Endomorphisms

In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also ＂uniform＂ with respect to C^1 perturbation.     

Quasi-shadowing Property on Random Partially Hyperbolic Sets

In this paper we investigate the quasi-shadowing property for C~1 random dynamical systems on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}_(-∞)~(+∞)on a random partially hyperbolic set there exists a "center" pseudo orbit {yk}_(-∞)~(+∞)shadowing it in the sense that yk+1 is obtained from the image of yk by a motion along the center direction. Moreover, when the random partially hyperbolic set has a local product structure, the above "center" pseudo orbit {yk}_(-∞)~(+∞)can be chosen such that yk+1 and the image of yk lie in their common center leaf.     

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

1IntroductionThispaperisconcernedwithpositivesolutionOfthesemilinearheatequationswithlocalizedreactionssubjecttoeitherinitialconditions(Cauchyproblem)ortheinitialandboundary-value(DirichletorNeumanntype)conditionswherenisaboundeddomaininRe,icEO.Equations(1.1)canbethoughtofasamodeltodescribesomephysicalphenomena(heatpropagation,chemicalreaction)inwhichthenonlinearreactionsinadynndcalsystemtakesplaceonlyatasinglesite.InthesequelforconvenienceweshallsamplycalltheCauchy,initial-Direchlet,orini…     

Train tracks with C 1+ self-renormalizable structures

We prove a one-to-one correspondence between C ¹⁺  conjugacy classes of diffeomorphisms with hyperbolic sets contained in surfaces and stable and unstable pairs of one-dimensional C ¹⁺  self-renormalizable structures.     

Rn上无奇点C1流的强极限跟踪性

本文证明了Rⁿ上无奇点C¹流的双曲集附近具有强极限跟踪性。     

随机环境中具有迁入的分枝过程的时序估计量的性质

讨论时序估计量^m(c)~、m(c)期望、方差,得出估计量^2σn的渐近性质和估计量^mNc的一致渐近正态性.     

误差项为指数白噪声的平稳AR(1)过程的贝叶斯分析

本文研究了一类误差项为指数白噪声的平稳自回归模型的参数估计问题.利用贝叶斯方法,获得了参数的后验分布及在平方损失下的贝叶斯估计结果,推广了Turkman的结果.     

一种保形C~1三次样条插值方法

本文得到了构造一个保形Ｃ１三次插值样条函数的充要条件，并给出了一种构造保形Ｃ１三次插值样条函数的方法．     

Local C1 solutions to some non‐linear PDE system

We prove that the quasilinear initial value problem (1) has a unique, local in time, C¹ solution, if the matrices A_i are diagonalizable and commute with each other. Copyright © 2006 John Wiley & Sons, Ltd.     

一类拟线性双曲型方程组混合初-边值问题的半整体C~1解

本文证明了具零特征且形式更广泛的一类拟线性双曲型方程组的具有一般非线性边界条件的混合初 一边值问题半整体C1解的存在唯一性.     

含退化边三角剖分下二元三次C1样条空间的维数

<正>1二元三次一阶光滑样条函数二元样条函数空间在数值逼近、曲面拟合、有限元方法(FEM)、散乱数据插值、多元数值积分、微分和积分方程数值解、计算机辅助几何设计(CAGD)、计算机图形学、信号过程和数学模型等领域有着广泛的应用.而空间S_3~1(Δ)除了二元三次样条函数具有的计     

Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics

We prove that the Cº boundedness of solution implies the global existence and uniqueness of C¹ solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C¹ solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.