本文選題：Bowen維數(shù)熵 + Packing維數(shù)熵�。� 參考：《合肥工業(yè)大學(xué)》2017年碩士論文

【摘要】：本文主要討論了Z~d-作用下拓?fù)鋭?dòng)力系統(tǒng)中的拓?fù)潇?研究了幾種不同定義下的拓?fù)潇氐囊恍┗拘再|(zhì)。具體安排如下:在緒論中,我們簡(jiǎn)要的介紹了拓?fù)鋭?dòng)力系統(tǒng)的起源及發(fā)展現(xiàn)狀,說(shuō)明本文所做的工作。在第二章中,我們介紹了本文所涉及的拓?fù)鋭?dòng)力系統(tǒng)和維數(shù)理論的一些基本概念和結(jié)論。在第三章中,總結(jié)了在Z作用下,不同方式定義的拓?fù)潇氐幕靖拍钆c性質(zhì)。在第四章中,我們研究Z~d-作用下幾種不同的拓?fù)潇?Bowen維數(shù)熵,Packing維數(shù)熵和Bowen集熵。對(duì)Bowen維數(shù)熵,我們證明了X的任意子集的Bowen維數(shù)熵可以由該子集的點(diǎn)的測(cè)度下局部熵來(lái)估計(jì):設(shè)m是X上的Borel概率測(cè)度,E是X上的Borel子集,且0＜s＜∞.(1)若h_μ(x)≤s對(duì)所有的x∈E成立,則h_(top)~B(E)≤s。(2)若h_μ(x)≥s對(duì)所有的x∈E成立,且μ(E)＞0,則h_(top)~B≥s。對(duì)Packing維數(shù)熵,我們也證明了類(lèi)似的結(jié)果:設(shè)μ是X上的Borel概率測(cè)度,E是X上的Borel子集,且0＜s＜∞,若h*_μ(x)≤s對(duì)所有的x∈E成立,則h_(top)~B(E)≤s。進(jìn)一步我們研究了Z~d-作用下Bowen維數(shù)熵,Packing維數(shù)熵和Bowen集熵三者間的關(guān)系。在第五章中,我們對(duì)本文研究的結(jié)果做了簡(jiǎn)要總結(jié),對(duì)今后可能研究的問(wèn)題作進(jìn)一步展望。
[Abstract]:In this paper, we mainly discuss the topological entropy in the topological dynamical system under the action of Znd-, and study some basic properties of the topological entropy under several different definitions. The specific arrangements are as follows: in the introduction, we briefly introduce the origin and development of topological dynamic system, and explain the work done in this paper. In the second chapter, we introduce some basic concepts and conclusions of topological dynamical system and dimension theory. In the third chapter, we summarize the basic concepts and properties of topological entropy defined in different ways under the action of Z. In the fourth chapter, we study several different topological entropy: Bowen-dimensional entropy packing dimension entropy and Bowen set entropy under the action of ZGD-. For the Bowen dimension entropy, we prove that the Bowen dimension entropy of any subset of X can be estimated from the local entropy under the measure of the point of the subset: let m be the Borel probability measure on X E is the Borel subset on X. And 0 < s < 鈭，

本文編號(hào)：1938988