This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
Focusing on elementary classical mechanics, this Problems and Solutions book is tailored for beginning university mathematics students, eliminating the need for prior physics knowledge. It serves as an accessible introduction to the subject, paving the way for advanced studies in Lagrangian, Hamiltonian, and quantum mechanics. The text emphasizes the importance of understanding foundational concepts to enhance comprehension of modern mathematical research areas, including symplectic geometry and spectral theory, linking classical mechanics to contemporary mathematical issues.
The book focuses on ordinary differential equations, a fundamental subject in undergraduate mathematics that follows calculus and linear algebra. It caters not only to mathematics majors but also to students from physical sciences, social sciences, and engineering. Despite the evolving applications of the topic across various disciplines, the course content has remained largely unchanged, reflecting a traditional approach to teaching this essential area of study.
Focusing on the interplay between global bifurcations and chaotic behavior in dynamical systems, this book presents analytical methods for understanding complex phenomena. It delves into theoretical frameworks and practical applications, offering insights into how bifurcations can lead to chaos in various systems. The text is designed for researchers and practitioners, providing rigorous mathematical approaches and examples that illustrate the significance of bifurcations in the study of chaos across different fields.
Focusing on the dynamics of non-linear systems, this monograph introduces a realistic framework for understanding phase space transport issues in applied dynamical systems. It begins with an exploration of transport in two-dimensional Poincaré Maps, addressing time-periodic perturbations of planar Hamiltonian systems. The work progresses to non-perturbative frameworks, expanding concepts to higher dimensions and varied time dependencies. This book is a significant resource for those interested in the mathematical applications within dynamical systems.
Focusing on elementary classical mechanics, this book is tailored for beginning university mathematics students, eliminating the need for prior physics knowledge. It serves as an introductory exploration, paving the way for more advanced studies in Lagrangian, Hamiltonian, and quantum mechanics. The text emphasizes the relevance of classical mechanics to modern mathematical research, highlighting how foundational concepts enrich understanding in areas like symplectic geometry and spectral theory.
In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds. Their techniques are based on an infinite dimensional generalisation of the graph transform and can be viewed as an infinite dimensional generalisation of Fenichels results. As such, they may be applied to a broad class of infinite dimensional dynamical systems.