【作者】 张金莲；

【导师】 何连法；

【作者基本信息】 河北师范大学 ， 基础数学， 2005， 博士

【摘要】 本文主要包含如下四部分内容。 第一部分（第二章）,着重研究非自治动力系统的原像熵。分别应用开覆盖和分离集、生成集给出了紧致空间上的连续自映射序列的原像熵的定义。讨论了这些原像熵之间及它们与拓扑熵之间的关系,得到了联系这些熵的不等式。并证明了这些熵都是等度拓扑共轭不变量,满足次可加性和次可乘性。对可扩的连续自映射序列而言,两类点原像熵相等,原像分枝熵与原像关系熵也相等。还证明了对（a）。由闭Riemann流形上的一个扩张映射经充分小的C¹—扰动生成的自映射序列,以及（b）。有限图上等度连续的连续自映射序列,有零原像分枝熵。 第二部分（第三章）,对连续半流的原像熵进行了研究。应用强分离集、弱生成集给出了紧致空间上的连续半流的点原像熵和原像分枝熵的定义。证明了对于无不动点的连续半流而言,这些原像熵具有一定程度的拓扑共轭不变性。得到了联系这些熵的不等式。还证明了连续半流与其时刻1映射具有相同的拓扑熵和原像熵。作为应用,证明了连续映射的拓扑熵和原像熵具有一定程度的扭扩不变性。 第三部分（第四章）,着重研究了圆周上单调映射序列的拓扑熵。证明了圆周上等度连续的单调映射序列f_1,∞={f_i}_i=1^∞的拓扑熵作为应用,得到了平环和环面上特殊的斜积变换的拓扑熵的估计,并证明了二维光滑闭流形上的C¹微分同胚与其在球丛上的扩充系统的拓扑熵一致。 第四部分（第五章）,对熵可扩映射和熵可扩流的拓扑压进行了研究。利用对生成集基数的估计得到了熵可扩映射的拓扑压和测度压的简化计算公式。证明了对流和其时刻1映射而言,熵可扩性是一种不变性质。并由此得到了熵可扩流的拓扑压的简化计算公式。更多还原

【Abstract】 There are four main parts in this paper.In the first part （Chapter 2）, we study the preimage entropies of nonautonomous dynamical systems. four entropy-like invariants for nonautonomous discrete dynamical systems given by a sequence of continuous selfmaps of a compact space are introduced and studied. We Proved that these entropies are all invariant with respect to equiconjugacy, and they all satisfy subadditivity and submultiplicativity. The relations between these entropies are established. We get that for expansive nonautonomous systems, two types of pointwise preimage entropies are equal, and the preimage branch entropy and the preimage relation entropy are equal too. We also get that two classes of nonautonomous systems: （a）. a sequence of small C¹-perturbations of an expanding map on a closed Riemmanian manifold, and （b）. a sequence of equicontinuous maps defined on a finite graph, have zero preimage branch entropy.In the second part（Chapter 3）, we consider the preimage entropies for continuous semi-flow of a compact metric space. We prove that most of these entropies are invariant in a certain sense under conjugate when the semi-flows under consideration are free of fixed points, and get an inequality relating these entropies. We also show that most of these entropies for semi-flow are consistent with that for its time-1 mapping. As applications, the relation between the entropies for a continuous map and for its suspension is given.In the third part （Chapter 4）, we study the topological entropy of a sequence of monotone maps on circles. We prove that the topological entropy of a sequence ofequicontinual monotone maps f₁,∞ = {f_i}_i=1^∞ is h（f₁,∞） = lim sup.As applications, we give the estimation of the entropies for some skew product on anular and Torus. And also show that a C¹ diffeomophism / on a 2-dimmensional smooth and closed Riemannian Manifold and its extension on the ball-bundle have the same entropy.In the fourth part （Chapter 5）, we study the pressure of the entropy-expansive更多还原