非自治动力系统拓扑熵的估计及非紧非自治逆紧拓扑压

发布时间：2018-02-05 19:29

本文关键词： 非自治动力系统拓扑熵拓扑压逆紧映射　出处：《西北大学》2015年硕士论文　论文类型：学位论文

【摘要】：拓扑熵是紧致拓扑空间中每个连续映射对应着的无穷大或非负实数,它是迄今为止唯一的拓扑共轭数值不变量,因此多年来一直受到数学、理论物理等领域中有关专家的普遍关注.而估计和计算拓扑熵是动力系统研究的一个重要课题,本文首先在自治动力系统中引入了指数扩张概念,并证明了指数扩张蕴含拓扑熵指数收敛,从而得到了指数扩张是E.Ghys等式成立的充分条件.其次,本文在非自治动力系统中定义了上(下)确界拓扑熵,并分别对拓扑熵、上(下)确界拓扑熵进行了估计.而拓扑压是拓扑熵的推广,它在热力学形式及维数理论中有着广泛的应用.因此,本文最后在非紧非自治逆紧动力系统上分别定义了拓扑压、上(下)容量拓扑压,并研究了它们的相关性质.
[Abstract]:Topological entropy is the infinite or non-negative real number corresponding to every continuous mapping in compact topological space. It is the only topological conjugate numerical invariant so far, so it has been subjected to mathematics for many years. The estimation and calculation of topological entropy is an important subject in the study of dynamical systems. In this paper, the concept of exponential extension is first introduced into autonomous dynamical systems. It is proved that exponential extension implies topological entropy exponential convergence, and a sufficient condition that exponential extension is the holding of E. Ghys equation is obtained. In this paper, we define the upper (lower) bound topological entropy in nonautonomous dynamical systems, and estimate the topological entropy of the upper (lower) bound respectively. The topological pressure is a generalization of the topological entropy. It has been widely used in thermodynamics and dimension theory. Therefore, in the end of this paper, topological pressure and upper (lower) capacity topological pressure are defined on noncompact nonautonomous inverse compact dynamical systems. Their related properties are also studied.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O19

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