7 Best Books on Hamiltonian Systems

We have compiled a list of the Best Reference Books on Hamiltonian Systems, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of Hamiltonian Systems Books with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Hamiltonian Systems below.

1."Hamiltonian Dynamical Systems and Applications" by Walter Craig “Hamiltonian Dynamical Systems and Applications” Book Review: This book presents a comprehensive introduction to Hamiltonian dynamical systems, exploring their wide-ranging applications in real-world scenarios. It delves into the intricacies of low-dimensional problems, offering detailed insights. It covers a diverse range of research areas, including classical mechanics, continuum mechanics, and partial differential equations. The language used throughout the book is simple and easy to comprehend, making it accessible to students and educators from various undergraduate programs in engineering and science. Its primary focus is on catering to the needs of the target audience.
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2."Introduction to the Perturbation Theory of Hamiltonian Systems" by Oleg Zubelevich and Dmitry Treschev “Introduction to the Perturbation Theory of Hamiltonian Systems” Book Review: The aim of this book is to present a comprehensive introduction to the perturbation theory of Hamiltonian systems. It covers a broad range of systems in classical mechanics, physics, chemistry, and other fields. The book explores concepts and challenges related to problems of geometric optics and celestial mechanics, and offers a wealth of practical examples with thorough explanations. It is intended primarily for students, teachers, and professionals working in diverse areas of engineering and science.
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3."Construction of Mappings for Hamiltonian Systems and Their Applications" by Sadrilla S Abdullaev S “Construction of Mappings for Hamiltonian Systems and their Applications” Book Review: The focus of this book is to present a thorough account of the construction of mapping for Hamiltonian systems and its numerous applications. It covers topics such as the method of canonical transformation of variables, classical perturbation theory, chaos in physical problems described by Hamiltonian systems, and mathematically-rigorous methods to construct symplectic mappings. Additionally, the book highlights how the dynamics of continuous Hamiltonian systems can be replaced by discrete ones. This book caters to students, teachers, and professionals in diverse fields of engineering and science, providing a valuable resource for anyone interested in this subject matter.
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4."Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations" by Allan C Peterson “Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations” Book Review: This book offers a comprehensive introduction to discrete Hamiltonian systems, covering topics such as difference equations, continued fractions, and Riccati equations. It provides detailed mathematical and theoretical explanations for each topic, assuming that the reader has a basic understanding of matrix theory. The book explores the existence and uniqueness theorem and requires an understanding of the implicit function theorem. In addition, there are detailed chapters on continued fractions. This book is designed for students, teachers, and professionals in various fields of engineering and science.
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5."Periodic Solutions of Hamiltonian Systems and Related Topics" by Antonio Ambrosetti “Periodic Solutions of Hamiltonian Systems and Related Topics” Book Review: This book offers a comprehensive examination of periodic solutions for Hamiltonian systems and associated subjects. It examines current breakthroughs in finding periodic solutions for second-order dynamical systems that have peculiar potentials. The book presents mathematical and theoretical justifications for a range of solutions to Hamiltonian systems, written in a clear and concise language for easy comprehension. It offers numerous practical instances with in-depth explanations to help readers enhance their understanding. The book aims to cater to the needs of students, teachers, and professionals across various fields of science and engineering.
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6."Foundation of Hamiltonian Systems" by Soh Edwin Mukiawa and Guy Degla “Foundation of Hamiltonian Systems” Book Review: This book offers a comprehensive introduction to the basics of Hamiltonian systems. It covers the fundamentals of Hamiltonian systems in both Euclidean and Hilbert spaces, demonstrating the existence of solutions for all autonomous Hamiltonian systems that are finite dimensional. It characterizes these solutions using initial conditions and class C2 with bounded gradient, and discusses the existence of periodic solutions for Hamiltonian systems. The book caters to students, educators, and professionals in various disciplines of science and engineering, and has been designed accordingly. advertisement advertisement
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7."Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces" by Hans J Zwart Birgit Jacob Zwart Jacob “Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces” Book Review: The main focus of this book is to provide an all-inclusive outline on linear port-Hamiltonian systems on infinite-dimensional spaces. It offers a self-sufficient introduction to the theory of infinite-dimensional systems, as well as discusses its application to port-Hamiltonian systems. The book emphasizes an abstract functional analytical method that is effectively combined with a physical approach to Hamiltonian systems. Furthermore, it highlights a combined approach that results in straightforwardly verifiable stability conditions. This book has been specifically designed for students, teachers, and professionals working in a wide range of fields in engineering and science.
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