Normal forms and stability of Hamiltonian systems / Hildeberto E. Cabral, Lúcia Brandão Dias.
2023
QA614.83
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Title
Normal forms and stability of Hamiltonian systems / Hildeberto E. Cabral, Lúcia Brandão Dias.
ISBN
9783031330469 (electronic bk.)
3031330463 (electronic bk.)
9783031330452
3031330455
3031330463 (electronic bk.)
9783031330452
3031330455
Published
Cham : Springer, 2023.
Language
English
Description
1 online resource (xxi, 337 pages) : illustrations (some color).
Item Number
10.1007/978-3-031-33046-9 doi
Call Number
QA614.83
Dewey Decimal Classification
515/.39
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed August 17, 2023).
Added Author
Brandão Dias, Lúcia, author.
Series
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 218. 2196-968X
Available in Other Form
Print version: 9783031330452
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Table of Contents
Foreword
Preliminaries on Advanced Calculus
Hamiltonian Systems Theory
Normal Forms of Hamiltonian Systems
Spectral Decomposition of Hamiltonian Matrices
The General Linear Normalization
Stability of Equilibria
Stability of Linear Hamiltonian Systems
Parametric Resonance
References
Index.
Preliminaries on Advanced Calculus
Hamiltonian Systems Theory
Normal Forms of Hamiltonian Systems
Spectral Decomposition of Hamiltonian Matrices
The General Linear Normalization
Stability of Equilibria
Stability of Linear Hamiltonian Systems
Parametric Resonance
References
Index.