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: 2023-08-12
  • 售價: $3,500
  • 貴賓價: 9.5 折 $3,325
  • 語言: 英文
  • 頁數: 337
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031330455
  • ISBN-13: 9783031330452

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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 stronglystable 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)

這本書介紹了哈密頓系統的研究，重點放在自主和週期系統的穩定性上，並擴展到通常在該領域的經典文獻中未涵蓋的主題。這本書源於在巴西佩爾南布科聯邦大學（被譽為哈密頓動力學理論領域的領先研究中心之一）所舉辦的講座和研討會。

本書以線性代數和高等微積分的一些結果的簡要回顧開始，接著介紹了哈密頓系統的基本理論。第三章涵蓋了哈密頓系統的正規形式的研究，而第四章和第五章則處理了哈密頓矩陣的正規化。非線性和線性系統的穩定性是第六章和第七章的主題。本書最後在第八章研究了參數共振。書中提供了所需的所有背景知識，從運動定律的哈密頓形式到強穩定系統的Krein-Gelfand-Lidskii理論的應用。

這本書以清晰、自成一體的方式呈現，對於高年級本科生、研究生以及從事這一主題研究的數學家和物理學家來說，是一個有價值的幫助。

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 是巴西佩南布科聯邦大學的名譽教授。他在1972年於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取得碩士學位。他的研究領域是動力系統，專注於哈密頓系統、天體力學、平衡穩定性和週期解。

Lúcia Brandão Dias 是巴西朗多尼亞聯邦大學的副教授。她於2007年在巴西佩南布科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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