Applied mathematical sciences (Springer-Verlag New York Inc.) ; Volume 218. [More in this series]

Applied Mathematical Sciences Series ; Volume 218

Summary note

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.

Bibliographic references

Includes bibliographical references and index.

Source of description

Description based on print version record.

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.

ISBN

3-031-33046-3

Doi

10.1007/978-3-031-33046-9

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