Описание: The definition of "photonics" has been broadened in recent years to include nonlinear and quantum optics, today usually based on laser light. This book covers the fundamental properties of photon and light beams, both experimentally and theoretically. It covers the essentials of linear interactions and most of the nonlinear interactions between light and matter in both the transparent and absorbing cases. It also provides a basic knowledge of modern lasers, as well as the principles of nonlinear optical spectroscopy. It is self-consistent and enriched by a large number of calculated illustrations, examples, and descriptive tables. Graduate students in physics and electrical engineering, as well as other sciences, will find this book a thorough introduction to the field, while for lecturers and scientists it offers a rich source of useful information and a ready-to-hand reference. About 4000 references open access to original literature.The second edition is completely revised and enlarged.
Автор: Haddad, Wassim M. Chellaboina, Vijaysekhar Название: Nonlinear dynamical systems and control ISBN: 0691133298 ISBN-13(EAN): 9780691133294 Издательство: Wiley Рейтинг: Цена: 23760.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. This graduate-level textbook is suitable for applied mathematicians, dynamical systems theorists, control theorists, and engineers.
Автор: Sanders J. A., Verhulst F., Murdock J. Название: Averaging Methods in Nonlinear Dynamical Systems ISBN: 0387489169 ISBN-13(EAN): 9780387489162 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added.Review of First Edition"One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews
Описание: From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2
Описание: This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as students of mathematics. This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry). Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.
Описание: Presents a grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to the developments in the field. This book begins with an introduction modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability.
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