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Bifurcation theory --- Congresses --- Congresses. --- Bifurcation theory - Congresses

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Bifurcation theory. --- Approximation theory.

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"Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided"--

Bifurcation theory --- Catastrophes (Mathematics)

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This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.

Cartography --- Bifurcation theory. --- Mathematical models.

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Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods, Second Edition is aimed at senior undergraduate and graduate students of aerospace and mechanical engineering. The book uses an optimal mix of physical insight and mathematical presentation to illustrate the core concepts of professional aircraft flight dynamics. An updated version of the aerodynamic model is presented with the corrected definition of rate (dynamic) derivatives, supported with examples of real-life airplanes and related data and by open-source computational tools. It introduces bifurcation and continuation methods as a tool for flight dynamic analysis. FEATURES Covers an up-to-date, corrected, clean' presentation of the elements of flight dynamics Presents a blend of theory, practice and application with real-life practical examples Provides a unique viewpoint of applied aerodynamicists and aircraft designers Introduces bifurcation and continuation methods as a tool for flight d ynamics analysis Includes a computational tool with real-life examples carried throughout the chapters The book is enriched with case studies of flight dynamics of a bird's flight, of a six-seater rigid-wing airplane from a design perspective, and airship dynamics to highlight the modal behaviour of similar-looking vehicles that are distinct from each other. Excerpts from reviews of the first edition: "Flight dynamics is a topic that can cause difficulties to aerospace engineering students. This text leads the reader gently through the material with plenty of practical examples and student exercises. As such, it is easy to follow the material and to gradually develop a deep understanding of a demanding topic. The book is ideal for undergraduate students and is a good text for graduate students."--James F. Whidborne, Cranfield University, United Kingdom "The book covers all the aspects of flight dynamics traditionally found in such texts interspersed with examples of the treatment of fe atures of current air vehicles ... In my opinion, this book covers the subject comprehensively and is a desirable reference source for undergraduates and graduates alike."--R.J. Poole, MRAeS, The Aeronautical Journal, June 2014 "The book design and the methodology of interpretation are directed to a wide range of target audience/population interested in studying the dynamics of flight. Given the scale and organization of information, the book will also be a useful tool in the analysis of flight dynamics for professionals in this field. The book is sure to appeal to anyone interested in the dynamics of flight."--Jaroslav Salga, Advances in Military Technology, June 2014

Aerodynamics --- Bifurcation theory --- Continuation methods