發(fā)布時(shí)間：2018-05-15 06:36

  本文選題：三維系統(tǒng) + 分段光滑�。� 參考：《上海師范大學(xué)》2017年碩士論文

【摘要】：本文考慮一類有一個(gè)不變平面的三維分段光滑系統(tǒng)且在這個(gè)不變平面上有一個(gè)k重閉軌.通過使用分支技巧和分析系統(tǒng)分支方程的解,我們研究了k重閉軌附近的特殊的分支現(xiàn)象并得到了從這個(gè)k重閉軌分支出周期軌的條件.此外,我們還研究了平面高次分段哈密頓系統(tǒng)的閉軌的重?cái)?shù).本文分為六章,具體內(nèi)容介紹如下:第一章主要介紹了所研究課題的實(shí)際背景,給出平面分段光滑系統(tǒng)的k重閉軌的定義.第二章主要介紹了與研究課題相關(guān)的一些基本概念和引用一些已有結(jié)果來作為本文的引理.第三章用曲線坐標(biāo)變換對(duì)原系統(tǒng)進(jìn)行處理,進(jìn)而得到處理后系統(tǒng)的分支方程.第四章通過分析分支方程的解來研究系統(tǒng)的極限環(huán).進(jìn)一步地,我們得到極限環(huán)存在的條件.第五章研究了平面高次分段哈密頓系統(tǒng)的閉軌的重?cái)?shù).對(duì)于哈密頓函數(shù)是一個(gè)高次多項(xiàng)式的分段系統(tǒng),我們得到了其閉軌重?cái)?shù)的上界.第六章給出了一個(gè)具體的三維分段光滑系統(tǒng),通過前面的定理,我們分析了其閉軌附近的極限環(huán).此外,我們還給出了一個(gè)具體的二維分段哈密頓系統(tǒng)并得到了其閉軌的最大重?cái)?shù).
[Abstract]:In this paper, we consider a three dimensional piecewise smooth system with an invariant plane and have a K closed orbit on this invariant plane. By using the branch technique and analyzing the solution of the bifurcation equation of the system, we have studied the special branch phenomena near the K closed rail and obtained the conditions for the bifurcation of the periodic rails from the K closed rail. The weight of the closed orbit of a planar higher-level Hamiltonian system is also studied. This paper is divided into six chapters. The specific content is introduced as follows: the first chapter introduces the actual background of the subject, and gives the definition of the K closed orbit of a planar piecewise smooth system. The second chapter introduces some basic concepts and references related to the research topic. The results have been used as the lemma in this paper. The third chapter deals with the original system by curvilinear coordinate transformation, and then obtains the branch equation of the system after processing. The fourth chapter studies the limit cycle of the system by analyzing the solution of the branch equation. Further, we get the condition of the existence of the limit ring. The fifth chapter studies the high order piecewise Hamilton. The weight number of the closed orbit of the system. The Hamilton function is a piecewise system of a high order polynomial. We get the upper bound of the number of closed orbit. In the sixth chapter, a concrete three-dimensional piecewise smooth system is given. Through the previous theorem, we analyze the limit ring near the closed orbit. In addition, we give a specific two-dimensional partition. The Hamiltonian system is obtained and its maximum number of closed orbits is obtained.

【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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本文編號(hào)：1891377