The book introduces Hamiltonian systems, focusing on stability and expanding on topics not covered by the canonical literature. It covers normal forms, matrix normalization, non-linear and linear stability, parametric resonance, and the Krein-Gelfand-Lidskii theory of strongly stable systems. It is suitable for advanced undergraduate and graduate students and mathematicians and physicists doing research on the topic.

Format: Hardback
Length: 337 pages
Publication date: 12 August 2023
Publisher: Springer International Publishing AG

Hamiltonian Systems: Stability and Beyond

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 Chapter 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 Chapter 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.

Key Features

• Clear and self-contained exposition: This book is designed to be accessible to advanced undergraduate and graduate students, as well as mathematicians and physicists doing research on this topic.


• Focus on stability: The book focuses on the stability of autonomous and periodic systems, providing a comprehensive overview of the field.


• Expanded coverage: The book covers topics that are usually not covered by the canonical literature in the field, making it a valuable resource for researchers.


• Lectures and seminars: The book emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, one of the leading research centers in the theory of Hamiltonian dynamics.


• Strongly stable systems: The book covers the Krein-Gelfand-Lidskii theory of strongly stable systems, which is essential for understanding the stability of Hamiltonian systems.

Contents

The book begins with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. Chapter 3 covers the study of normal forms of Hamiltonian systems, 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. Chapter 8 finishes with a study of parametric resonance.

Conclusion

This book is a valuable help to advanced undergraduate and graduate students, as well as mathematicians and physicists doing research on this topic. With its clear, self-contained exposition, it provides a comprehensive overview of the field and covers topics that are usually not covered by the canonical literature. The book's focus on stability and expanded coverage make it a valuable resource for researchers in the field.

Dimension: 235 x 155 (mm)
ISBN-13: 9783031330452
Edition number: 1st ed. 2023