Overview
- Offers an introduction to the basic theory of Hamiltonian systems
- Of use to graduate students and researchers in mathematics and physics
- Written by well-known experts in the field
Part of the book series: Applied Mathematical Sciences (AMS, volume 218)
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About this book
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.
Keywords
Table of contents (8 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Normal Forms and Stability of Hamiltonian Systems
Authors: Hildeberto E. Cabral, Lúcia Brandão Dias
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-031-33046-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-33045-2Published: 12 August 2023
Softcover ISBN: 978-3-031-33048-3Due: 12 September 2023
eBook ISBN: 978-3-031-33046-9Published: 11 August 2023
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: XXI, 337
Number of Illustrations: 16 b/w illustrations, 13 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Analysis, Mathematical Physics