| 1. | In chapter three , we study the topological entropy of the set of divergence points
在第三章中，我们主要研究了分叉点集合的拓扑熵。 |
| 2. | The first two chapters are about iterated function systems and the third one is about the topological entropy of a certain dynamical system
其中一，二两章是关于函数迭代系统，第三章是关于动力系统拓扑熵。 |
| 3. | Furthermore , we point out that for any interval lipschitz map with positive topological entropy there is a chaotic set with positive hausdorff dimension
特别指出，对具有正熵的lipschitz区间映射而言，存在正hausdorff维数的混沌集。 |
| 4. | The set of divergence points is defined as following : we obtain that either all has the same limiting point or the topological entropy of the divergence points is as big as the whole space x . we also study the topological entropy of sup sets
我们得到如果不是所有的点x x ， { l _ nx }有相同的极限点，则d ( f ， )的拓扑熵和整个空间的拓扑熵相同。此外我们还考虑了上集的拓扑熵。 |
| 5. | In this paper it is proved that there are no scramble sets with nonzero invariant probability measure and especially there are no sequence - distribution - scramble sets with nonzero invariant probability measure in the minimal mappings of a compace metric space and interval mappings with zero topological entropy
摘要证明紧度量空间的极小映射以及拓扑熵为零的区间映射不存在具有非零不变概率测度的混沌子集，特别不存在具有非零不变概率测度的序列分布混沌子集。 |
| 6. | Further - more , by constructing the relations between the fiflite subshift on the symbolic set and the chaotic iterated map by means of marotto theorem , we investigate the structure of the invariant as well as the estimation of topological entropy , zeta - - function , lyapunov exponent . by the end of the chapter , we present several conclusions on the perturbed chaotic systems and a theorem about " heteroclinical repellers imply chaos " . in chapter 3 , we are mathematically modelling two particular classes of impul - sive differential equations having chaos dynamics
在本文的第三章中，我们建立了脉冲微分方程中的两类混沌模型，一类利用映射的扰动理论证明了系统随着参数变化时具有不同意义的混沌动力学行为；另一类则利用勒贝格可测的概念给出了脉冲微分方程中所特有的关于脉冲间期函数初值敏感的定义，同时理论证明了在一类脉冲微分方程中确实如新定义所描述的复杂动力学行为 |
