一類受限符號(hào)系統(tǒng)的拓?fù)潇?/H1>
發(fā)布時(shí)間：2018-02-16 18:35
本文關(guān)鍵詞： 符號(hào)動(dòng)力系統(tǒng) 拓?fù)潇?有限型子移位 長(zhǎng)度約束 出處：《吉林大學(xué)》2017年碩士論文 論文類型：學(xué)位論文
【摘要】：在拓?fù)鋭?dòng)力系統(tǒng)領(lǐng)域,符號(hào)動(dòng)力系統(tǒng)是一個(gè)重要的研究方向,其中有限型子移位在理論與應(yīng)用中均具有重要意義,受到廣泛關(guān)注.關(guān)于有限型子移位,現(xiàn)在已經(jīng)有大量的研究成果,對(duì)于子移位拓?fù)潇氐难芯恳彩菬嶂兄?有限長(zhǎng)度的(d,k)約束系統(tǒng)被應(yīng)用于各種儲(chǔ)存系統(tǒng)和工業(yè)上復(fù)雜的機(jī)器運(yùn)行中,定義它為一個(gè){0,1}兩個(gè)符號(hào)的約束系統(tǒng),其中序列內(nèi)兩個(gè)相鄰的“1”中間連續(xù)“0”的數(shù)量有至多d個(gè)至少k個(gè),這樣的系統(tǒng)已經(jīng)被學(xué)者們研究,同時(shí)它也是一類空間有限型子移位,通過(guò)其特征多項(xiàng)式計(jì)算符號(hào)動(dòng)力系統(tǒng)的拓?fù)潇?這里用C(d,k)表示拓?fù)潇?簡(jiǎn)單總結(jié)下來(lái)不同(d,k)約束系統(tǒng)的拓?fù)潇乜梢韵嗟?這樣的等式有且僅有如下形式:C(d,2d)= C(d + 1,3d + 1),C(d + 1,∞)= C(d,2d + 1),d ≥ 0,C(1,2)= C(2,4)= C(3,7)= C(4,∞).本文主要研究的是一類{0,1}兩個(gè)符號(hào)的雙重約束下約束系統(tǒng),我們將其定義為雙重約束下的(p,q)-約束系統(tǒng)(簡(jiǎn)記為(p,q)-DUB).這里的(p,q)約束是指{0,1}序列中的符號(hào)最多連續(xù)出現(xiàn)p個(gè)“0”和q個(gè)“1”,記(p,q)-DUB系統(tǒng)的拓?fù)潇貫镃(p,q),(d,k)約束系統(tǒng)拓?fù)潇氐闹悼梢酝ㄟ^(guò)相應(yīng)的多項(xiàng)式的根得到,但是很難直接通過(guò)d,k的數(shù)值大小比較不同約束系統(tǒng)之間熵值的大小,但是對(duì)于(p,q)-DUB,我們找到了一個(gè)簡(jiǎn)單有效的方法很容易的比較任意兩個(gè)或者多個(gè)(p,q)-約束系統(tǒng)的拓?fù)潇氐拇笮?事實(shí)上,我們可以對(duì)所有(p,q)-約束系統(tǒng)的拓?fù)潇剡M(jìn)行排序,結(jié)論為:0 = C(1,1) C(1,2)... C(1,∞)= C(2,2) C(2,3)... C(2,∞)=C(3,3)C(3,4)......C(∞,∞)=ln 2.值得注意的,C(p,∞)=C(p+1,p+1)是(p,q)-DUB系統(tǒng)的拓?fù)潇匚ㄒ淮嬖诘牡仁?
[Abstract]:In the field of topological dynamical system, symbolic dynamical system is an important research direction, in which finite type subshift is of great significance in theory and application. There have been a lot of research results, and the study of the topological entropy of subshift is also very hot. The finite length of the constrained system has been applied to various storage systems and the complex machine operation in industry. It is defined as a constraint system with two symbols {0 ~ 1}, in which the number of two adjacent "1" continuous "0" in a sequence has not more than d at least k, such a system has been studied by scholars, and it is also a class of space finite type subshifts. The topological entropy of the symbolic dynamical system is calculated by its characteristic polynomial, and the topological entropy is expressed by Cndnk), and the topological entropy of different constrained systems can be equal. This equation has the following forms, and only in the following forms: C ~ (1) C ~ (1) C ~ (1) D ~ (2) C ~ (1) C ~ (1) C ~ (1) C ~ (1), 鈭，
本文編號(hào)：1516172
本文鏈接：http://sikaile.net/kejilunwen/yysx/1516172.html
本文關(guān)鍵詞： 符號(hào)動(dòng)力系統(tǒng) 拓?fù)潇?有限型子移位 長(zhǎng)度約束 出處：《吉林大學(xué)》2017年碩士論文 論文類型：學(xué)位論文
【摘要】：在拓?fù)鋭?dòng)力系統(tǒng)領(lǐng)域,符號(hào)動(dòng)力系統(tǒng)是一個(gè)重要的研究方向,其中有限型子移位在理論與應(yīng)用中均具有重要意義,受到廣泛關(guān)注.關(guān)于有限型子移位,現(xiàn)在已經(jīng)有大量的研究成果,對(duì)于子移位拓?fù)潇氐难芯恳彩菬嶂兄?有限長(zhǎng)度的(d,k)約束系統(tǒng)被應(yīng)用于各種儲(chǔ)存系統(tǒng)和工業(yè)上復(fù)雜的機(jī)器運(yùn)行中,定義它為一個(gè){0,1}兩個(gè)符號(hào)的約束系統(tǒng),其中序列內(nèi)兩個(gè)相鄰的“1”中間連續(xù)“0”的數(shù)量有至多d個(gè)至少k個(gè),這樣的系統(tǒng)已經(jīng)被學(xué)者們研究,同時(shí)它也是一類空間有限型子移位,通過(guò)其特征多項(xiàng)式計(jì)算符號(hào)動(dòng)力系統(tǒng)的拓?fù)潇?這里用C(d,k)表示拓?fù)潇?簡(jiǎn)單總結(jié)下來(lái)不同(d,k)約束系統(tǒng)的拓?fù)潇乜梢韵嗟?這樣的等式有且僅有如下形式:C(d,2d)= C(d + 1,3d + 1),C(d + 1,∞)= C(d,2d + 1),d ≥ 0,C(1,2)= C(2,4)= C(3,7)= C(4,∞).本文主要研究的是一類{0,1}兩個(gè)符號(hào)的雙重約束下約束系統(tǒng),我們將其定義為雙重約束下的(p,q)-約束系統(tǒng)(簡(jiǎn)記為(p,q)-DUB).這里的(p,q)約束是指{0,1}序列中的符號(hào)最多連續(xù)出現(xiàn)p個(gè)“0”和q個(gè)“1”,記(p,q)-DUB系統(tǒng)的拓?fù)潇貫镃(p,q),(d,k)約束系統(tǒng)拓?fù)潇氐闹悼梢酝ㄟ^(guò)相應(yīng)的多項(xiàng)式的根得到,但是很難直接通過(guò)d,k的數(shù)值大小比較不同約束系統(tǒng)之間熵值的大小,但是對(duì)于(p,q)-DUB,我們找到了一個(gè)簡(jiǎn)單有效的方法很容易的比較任意兩個(gè)或者多個(gè)(p,q)-約束系統(tǒng)的拓?fù)潇氐拇笮?事實(shí)上,我們可以對(duì)所有(p,q)-約束系統(tǒng)的拓?fù)潇剡M(jìn)行排序,結(jié)論為:0 = C(1,1) C(1,2)... C(1,∞)= C(2,2) C(2,3)... C(2,∞)=C(3,3)C(3,4)......C(∞,∞)=ln 2.值得注意的,C(p,∞)=C(p+1,p+1)是(p,q)-DUB系統(tǒng)的拓?fù)潇匚ㄒ淮嬖诘牡仁?
[Abstract]:In the field of topological dynamical system, symbolic dynamical system is an important research direction, in which finite type subshift is of great significance in theory and application. There have been a lot of research results, and the study of the topological entropy of subshift is also very hot. The finite length of the constrained system has been applied to various storage systems and the complex machine operation in industry. It is defined as a constraint system with two symbols {0 ~ 1}, in which the number of two adjacent "1" continuous "0" in a sequence has not more than d at least k, such a system has been studied by scholars, and it is also a class of space finite type subshifts. The topological entropy of the symbolic dynamical system is calculated by its characteristic polynomial, and the topological entropy is expressed by Cndnk), and the topological entropy of different constrained systems can be equal. This equation has the following forms, and only in the following forms: C ~ (1) C ~ (1) C ~ (1) D ~ (2) C ~ (1) C ~ (1) C ~ (1) C ~ (1), 鈭，
本文編號(hào)：1516172
本文鏈接：http://sikaile.net/kejilunwen/yysx/1516172.html
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