KAM Theory for Lower Dimensional Tori

定　價：￥48.00

作　者：	劉柏楓著
出版社：	西南財大出版社
叢編項：
標　簽：	經(jīng)濟貿(mào)易政策

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ISBN：	9787550415911	出版時間：	2015-11-01	包裝：	平裝
開本：	16開	頁數(shù)：		字數(shù)：

內(nèi)容簡介

　　劉柏楓編*的《KAM Theory for Lower-Dimensional Tori》討論了在經(jīng)典的KAM理論中幾個沒有討論的問題。主要介紹KAM理論中的低維不變環(huán)面的保持性。介紹了廣義Hamilton系統(tǒng)雙曲型低維不變環(huán)面和具有一般形式的廣義Hamilton系統(tǒng)的低維不變環(huán)面的保持性。介紹了具有擬周期攝動的近可積Hamilton系統(tǒng)的KAM理論。介紹了具有相交性小扭轉(zhuǎn)的辛映射的不變環(huán)面的保持性。介紹了辛映射的雙曲型低維不變環(huán)面的保持性定理。

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圖書目錄

Chapter 1 Hamiltonian Mechanics
1.1 The Basic Concepts Of Dynamical System
1.2 Differential Form
Chapter 2 Hamiltonian System
2.1 Classical Hamiltonian and Generalized Hamiltonian
2.2 Completely Integrable Systems and Nearly Integrable Systems
Chapter 3 KAM Theorem
3.1 The Classical KAM Theorem
3.2 Lower-Dimensional KAM Theorem
3.3 The Generalized KAM Theorem
Chapter 4 Lower-Dimensional Invariant Tori in Hamiltonian Svstem
4.1 Introduction
4.2 KAM Step
4.3 Iteration Lemma
4.4 Proof of the Main Result
4.5 Example
Chapter 5 KAM-Type Theorem with a Quasi-Periodic Perturbation
5.1 Introduction
5.2 The KAM Step
5.3 Iteration Lemma
5.4 Proof of the Main Result
5.5 Some Examples
Chapter 6 The Persistence of Lower-Dimensional Tori for Generalized Hamiltonian
6.1 Introduction and Main Result
6.2 KAM Step
6.3 Iteration Lemma
6.4 Proof of the Main Result
Chapter 7 Hyperbolic Invariant Tori for Generalized Hamiltonian Systems
7.1 Introduction and Main Result
7.2 KAM Step
7.3 Iteration Lemma
7.4 Proof of the Main Result
7.5 Examples
Chapter 8 The Hyperbolic Invariant Tori of the Symplectic Mappings
8.1 Introduction
8.2 Outline of the Proof of Theorem 8.1.1
8.3 Estimates in One Step
8.4 Iteration Lemma
8.5 Proof of the Main Result
Chapter 9 Appendix
9.1 Some Facts About Analytic Functions
9.2 Technical Lemma
Bibliography