Normal Forms and Stability of Hamiltonian Systems

Cabral, Hildeberto E., Brandão Dias, Lúcia

Normal Forms and Stability of Hamiltonian Systems
  • 出版商: Springer
  • 出版日期: 2024-08-13
  • 售價: $2,350
  • 貴賓價: 9.5 折 $2,233
  • 語言: 英文
  • 頁數: 337
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303133048X
  • ISBN-13: 9783031330483

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商品描述

This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics.

This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems.

With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.

商品描述(中文翻譯)

本書向讀者介紹哈密頓系統的研究，重點關注自主系統和週期系統的穩定性，並擴展到通常不在該領域的經典文獻中涵蓋的主題。這本書源自於在巴西佩南布科聯邦大學舉辦的講座和研討會，該校被認為是哈密頓動力學理論的主要研究中心之一。

本書首先簡要回顧了一些線性代數和高等微積分的結果，接著介紹哈密頓系統的基本理論。哈密頓系統的標準型研究在第三章中進行，而第四章和第五章則處理哈密頓矩陣的正規化。第六章和第七章探討非線性和線性系統的穩定性。本書最後在第八章中研究參數共振。所有所需的背景知識都已呈現，從哈密頓運動定律的公式化到Krein-Gelfand-Lidskii強穩定系統理論的應用。

本書以清晰且自成體系的方式呈現，對於高年級本科生、研究生，以及從事相關研究的數學家和物理學家來說，都是一個寶貴的幫助。

作者簡介

Hildeberto Cabral is an Emeritus Professor at the Federal University of Pernambuco, Brazil. He did his PhD at the University of California, Berkeley (1972), after getting a Master's degree from the Institute of Pure and Applied Mathematics-IMPA, Brazil. He does research on dynamical systems, focusing on Hamiltonian systems, celestial mechanics, stability of equilibria, and periodic solutions.

Lúcia Brandão Dias is an Associate Professor at the Federal University of Rondônia, Brazil. She holds a PhD in Mathematics (2007) from the Federal University of Pernambuco, Brazil, with post-doc studies at the same university. Her research interests lie in Hamiltonian systems, differential equations, and n-body problems.

作者簡介(中文翻譯)

Hildeberto Cabral 是巴西佩魯南聯邦大學的名譽教授。他於1972年在加州大學伯克利分校獲得博士學位，之前在巴西純粹與應用數學研究所（IMPA）獲得碩士學位。他的研究專注於動力系統，特別是哈密頓系統、天體力學、平衡穩定性和週期解。

Lúcia Brandão Dias 是巴西隆多尼亞聯邦大學的副教授。她於2007年在巴西佩魯南聯邦大學獲得數學博士學位，並在同一所大學進行博士後研究。她的研究興趣包括哈密頓系統、微分方程和n體問題。

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