逆极限空间的伪轨跟踪性

证明了对于由｛Ｘｉ,ｉ,ｆｉ｝ｉ＝１生成的逆极限系统（Ｘ∞,ｆ∞）,如果每个ｆｉ具有伪轨跟踪性,则诱 导映射ｆ∞也具有伪轨跟踪性．并构造了一个例子说明它的逆命题不成立．还证明了零维紧致度量群 的自同构拓扑共轭于一族有限型子转移生成的逆极限系统．     

序列伪轨跟踪性与拓扑可迁

给出序列伪轨跟踪性的定义,得到拓扑可迁的一个充分条件,并证明,若f是同胚,则f具有序列伪轨跟踪性当且仅当其逆极限空间上的移位映射σf具有序列伪轨跟踪性。     

逆极限空间上渐近伪轨跟踪性质

The connection between APOTP （asymptotic pseudo orbit tracing property） for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is showed that the shift map on Henderson pseudoarc has APOTP.     

伪轨跟踪与混沌

本文对具有无限个点的紧致度量空间上的连续满射，研究了伪轨跟踪性质与Ｒｕｅｌｌｅ－Ｔａｋｅｎｓ意义下的混沌、拓扑混合及具有性质Ｐ的关系．     

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。     

逐点伪轨跟踪性质及其应用

本文给出紧致度量空间逐点伪轨跟踪性质的定义,该定义是伪轨跟踪性质定义的推广.作为应用,证明如下结论:(i)若f具有逐点伪轨跟踪性质,且对任意k∈Z ,fk为链转换的,那么对任意k∈Z ,fk为开集转换;(ii)若f具有逐点伪轨跟踪性质,且对任意n∈Z ,fn为链转换的,则f具有初始敏感依赖性质;(iii)若f为开集混合的,且具有逐点伪轨跟踪性质,那么f具有性质P;(iv)设f:(X,d)→(X,d)是同胚映射,那么f具有逐点伪轨跟踪性质当且仅当移位映射σf具有逐点伪轨跟踪性质.     

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f具有极限跟踪性.     

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.     

迭代函数系统的伪轨特殊性和平均跟踪性质

研究了迭代函数系统IFS(F)的伪轨特殊性与平均跟踪性质.结合经典动力系统的相关方法,证明了:如果IFS(F)有伪轨特殊性质,则它有平均跟踪性质;如果IFS(F)有平均跟踪性质并且F中某些f有稠密的0-回复点,则IFS(F)是拓扑传递的.     

符号空间及逆极限空间上的正混沌

本文推广Ｌｉ－Ｙｏｒｋｅ混沌定义,给出正混沌的定义,得到一类描述正混沌的符号动力 系统．并证明紧致度量空间上的连续映射正混沌的充要条件是其逆极限空间上的移位映射是 正混沌的．     

具有跟踪性可扩流的周期轨的双曲性

证明了具有跟踪性的可扩流在其周期轨附近的拓扑动力性质与双曲周期轨相同.     

Differentiability of Inverse Operators and Limit Theorems for Inverse Functions

Let H be a map from a set SR ^d to R ^d . For tR ^d let _H (t) denote the distance from t to the set H(S). Consider sequences {s _n} _n1 in S such that . Any limit point of any such sequence (finite or infinite) is considered as a possible value of the inverse H ^–1(t). Any map defined in such a way will be called an SC-inverse (a selected closest inverse) to H. In the paper we study differentiability of the nonlinear operator at H=G, where G is a one-to-one map from S onto a set TR ^d with good analytic properties (specifically, a diffeomorphism). We establish compact differentiability of this operator tangentially to continuous functions and introduce a family of norms such that it is Fréchet differentiable with respect to them. We also obtain optimal bounds for the remainder of the differentiation, extending to the multivariate case recent results of Dudley. These differentiability results are applied to random maps , which could be statistical estimators of an unknown map G. For a function J on R ^d , let (J) _T be its restriction to T. It is shown that for a diffeomorphism G and for an increasing sequence of positive numbers {a _n } _n1 weak convergence of the sequence {a _n (G _n – G)} _n1 (locally in S) is equivalent to weak convergence of the sequence (locally in T) along with the convergence of the sequence to 0 in probability (locally uniformly in S). The equivalence holds for all SC-inverses and all double SC-inverses and it extends to the multivariate case a theorem of Vervaat. Moreover, each of these equivalent statements implies a kind of Taylor expansion of the SC-inverse at G (locally uniformly in T) where inv(A) denotes the inverse of a nonsingular linear transformation A in R ^d . Such limit theorems for functional inverses can be used to study asymptotic behavior of statistical estimators defined implicitly (as solutions of equations involving the empirical distribution P _n ). We show how to apply this approach to get asymptotic normality of M-estimators in the multivariate case under minimal assumptions. We consider an extension of the quantile function to the multivariate case related to M-parameters of a distribution P in R ^d (an M-quantile function)and use limit theorems for functional inverses to study limit behavior of the empirical M-quantile process. We also show how to use these theorems to study asymptotics of regression quantiles.     

紧度量空间上轨道的分类和极限集有向同伦不变性

本文利用正半轨道的ω极限集对紧度量空间的正半轨道进行分类,并讨论不动点和周期点的存在性.最后,引入轨道的正半同伦和负半同伦的概念,证明ω极限集和ω极限集在正半同伦和负半同伦的条件下是不变的,从而导出不动点和周期点在正半同伦和负半同伦的条件下保持不变.     

具有未知源的某些非线性伪抛物型方程的反问题

考 虑具有未 知源项的 某些非 线性伪 抛物 型方程 的反演 问题． 首先 将伪抛 物型 方程初 边值问 题化为非线 性发展方 程 Ｃｏｕｃｈ ｙ 问题,然 后,利用半 群理论,论 证发展 方程反问 题解的存 在唯一 性,最后, 利用不 动点方法得到 伪抛物型方程反 问题的可解性     

Limit Theorems for Inverse Process T_n of Hawkes Process

We consider linear Hawkes process N_t and its inverse process T_n. The limit theorems for N_t are well known and studied by many authors. In this paper, we study the limit theorems for T_n. In particular, we investigate the law of large numbers, the central limit theorem and the large deviation principle for T_n. The main tool of the proof is based on immigration-birth representation and the observations on the relation between N_t and T_n.     

一类生物复制网络的极限性质

本文考虑生物网络中一类复制模型度分布的极限性质.利用组合知识和概率论中鞅方法,讨论了度分布的大数定律和中心极限定理,为生物学家研究生物内部系统机制提供理论基础.     

On the Inverse Limit of Higson Compactifications

Higson have introduced the conception of "Higson's corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) < R}. Recall that a slowly oscillating function on X is a function f G C*(X) satisfying the following condition:     

σ-满正规空间的逆极限

本文证明:设X是逆系统(X_απ_β~α,A}的逆极限,|A|=λ,假设每个投射π_α:X→X_α是开且到上的。X是λ-仿紧和λ-可遮的,如果每个X_α是σ-满正规的(可遮的,σ-集体正规的),则X是σ-满正规的(可造的,σ-集体正规的)。作为这一结果的推论,我们还将证明正规σ-满正规性满足如文[1]中的通常形式的逆极限定理及遗传σ-满正规性的类似结果。