Normal Forms and Stability of Hamiltonian Systems

Name: Normal Forms and Stability of Hamiltonian Systems
Brand: Springer
SKU: 9783031330483
Price: 4360.0 INR
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by Hildeberto E. Cabral

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ISBN13: 9783031330483
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: August 13, 2024
Pages: 337
Original Price: EUR 59.99
Language: English
Edition: 2023
Item Weight: 510 grams
BISAC Subject(s): Mathematical Analysis, System Theory, and Differential Equations / General

About The Book

From the Back Cover

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.

About The Author

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.

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