發(fā)布時(shí)間：2019-03-12 10:54

【摘要】：正規(guī)形理論是研究非線性問題時(shí)廣泛采用的一種手段,無論是它自身的理論還是其應(yīng)用都具有特別重要的意義.近些年來,該理論在Hilbert第十六問題、分岔理論、動(dòng)力系統(tǒng)的分類問題以及微分同胚嵌入流問題等很多方面都得到了廣泛的應(yīng)用,這就使得它越來越引起人們的關(guān)注.本論文的研究?jī)?nèi)容主要由兩部分組成:第一部分研究了R3空間中在通有條件下映射在非強(qiáng)1-共振不動(dòng)點(diǎn)附近的多項(xiàng)式正規(guī)形和有限確定性;第二部分研究了R3空間中在退化條件下映射在非強(qiáng)1-共振不動(dòng)點(diǎn)附近的多項(xiàng)式正規(guī)形和有限確定性.本論文的第一部分主要對(duì)R3空間中在通有條件下線性部分系數(shù)矩陣含有重根的非強(qiáng)1-共振映射進(jìn)行研究.我們利用經(jīng)典的Poincare-Dulac正規(guī)形定理,主要通過討論映射的線性部分系數(shù)矩陣特征根的共振關(guān)系得到該類映射所對(duì)應(yīng)的經(jīng)典共振正規(guī)形.在Ichikawa關(guān)于映射的有限確定性理論基礎(chǔ)上,通過引進(jìn)一系列共振變換,結(jié)合Belistkii定理,討論了其有限確定性并得到了多項(xiàng)式正規(guī)形.本論文的第二部分主要對(duì)R3空間中在退化條件下線性部分系數(shù)矩陣不含有重根的非強(qiáng)1-共振映射進(jìn)行研究.我們同樣利用引入共振變換的方法,結(jié)合Ichikawa和Belistkii定理得到了該類映射在滿足一定的退化條件時(shí),可以與一個(gè)多項(xiàng)式正規(guī)形光滑等價(jià)并能有限確定.
[Abstract]:The formal theory is a kind of means to study the non-linear problem, whether it is its own theory or its application. In recent years, the theory has been widely used in many aspects such as Hilbert's sixteenth problem, the bifurcation theory, the classification of the power system and the problem of the embedded flow of the differential and the embryo, which makes it more and more concerned. The research contents of this paper are mainly composed of two parts: the first part studies the formal and finite certainty of the polynomial which is mapped on the non-strong 1-resonance fixed point in the R3 space; The second part studies the polynomial normal form and the finite certainty that are mapped on the non-strong 1-resonance fixed point in the R3 space under the condition of degradation. The first part of this paper mainly studies the non-strong 1-resonance mapping of the linear partial coefficient matrix containing the heavy root in the R3 space. In this paper, we use the classical Poincare-Dulac normal-shape theorem to obtain the classical resonance normal form corresponding to this kind of mapping by discussing the resonance relation of the linear part coefficient matrix characteristic root of the mapping. On the basis of Ichikawa's finite certainty theory about mapping, by introducing a series of resonance transforms, the finite certainty is discussed and the polynomial normal form is obtained by combining the Belistkii theorem. The second part of this paper mainly studies the non-strong 1-resonance mapping of the linear partial coefficient matrix without heavy root in the R3 space. In the same way, we use the method of introducing the resonance transformation, and in combination with the Ichikawa and the Belistkii theorem, this kind of mapping can be equivalent to the normal shape of a polynomial and can be determined in a finite way when certain degradation conditions are satisfied.
【學(xué)位授予單位】：北京工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O174.14

【共引文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 楊柳芳;平面映射的線性化及相關(guān)函數(shù)方程的C~1解問題[D];重慶師范大學(xué);2015年

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本文編號(hào)：2438710