【作者】 朱玉峻；

【导师】 何连法；

【作者基本信息】 河北师范大学 ， 基础数学， 2003， 博士

【摘要】 本文主要包含如下三部分内容。 第一部分(第二章)，着重研究连续映射和连续流的极限跟踪性。首先，给出了极限跟踪性的一些基本性质；其次，得到了n维欧氏空间上线性自同构及线性流具有极限跟踪性的特征；最后，作为应用证明了双曲环面自同态以及Smale“马蹄”在其不变集上具有极限跟踪性。 第二部分(第三章)，对Riemann流形上C~1自同态的Lipschitz跟踪性和反跟踪性进行了研究。证明了C~1自同态在其双曲不变集附近具有Lipschitz跟踪性，当C~1自同态为双曲时，对一类连续method而言具有反跟踪性，并且这两种跟踪性相对C~1小扰动均具有一致性。 第三部分(第四章)，着重研究C~1随机动力系统的跟踪性。对于由Oseledec乘法遍历定理得到的满测度(full measure)不变集定义了双曲性，并证明了系统在这个不变集上具有Lipschitz跟踪性。更多还原

【Abstract】 There are three main parts in this paper.In the first part（Chapter 2）, we study the limit shadowing property for continuous maps and continuous flows. Firstly, some basic properties of the limit shadowing are given; Secondly, we give the characterization of both lin-ear automorphisms and linear flows on Rⁿ with the limit shadowing property; Thirdly, as applications we prove that the hyperbolic endomorphisms on Tⁿ have the limit shadowing properties, Smale "horseshoes" have the same prop-erties on their invariant sets.In the second part（Chapter 3）, we consider the Lipschitz shadowing and the inverse shadowing for C¹ endomorphisms. We show that near a hyperbolic set a C¹ endomorphism has the Lipschitz 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 C¹ perturbation.In the third part （Chapter 4）, we consider the shadowing of C¹ random dynamical system. We define a type of hyperbolicity on the full measure invariant set which is given by the Oseledec’s multiplicative ergodic theorem and prove that the system has the Lipschitz shadowing property on it.更多还原