Topological Degree Approach to Bifurcation Problems (Topological Fixed Point Theory and Its Applications, 5) - Softcover
This book contains original bifurcation results for the existence of oscillations and chaotic behavior of differential equations and discrete dynamical systems under variation of involved parameters. It studies a broad variety of nonlinear problems.
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Topological bifurcation theory is one of the most essential topics in mathematics. This book contains original bifurcation results for the existence of oscillations and chaotic behaviour of differential equations and discrete dynamical systems under variation of involved parameters. Using topological degree theory and a perturbation approach in dynamical systems, a broad variety of nonlinear problems are studied, including: non-smooth mechanical systems with dry frictions; weakly coupled oscillators; systems with relay hysteresis; differential equations on infinite lattices of Frenkel-Kontorova and discretized Klein-Gordon types; blue sky catastrophes for reversible dynamical systems; buckling of beams; and discontinuous wave equations.
Precise and complete proofs, together with concrete applications with many stimulating and illustrating examples, make this book valuable to both the applied sciences and mathematical fields, ensuring the book should not only be of interest to mathematicians but to physicists and theoretically inclined engineers interested in bifurcation theory and its applications to dynamical systems and nonlinear analysis.
From the book reviews:
“This excellent and well-organized book is based on recently published papers of the author using topological degree methods. ... The book should not only be of interest to mathematicians but to physicists and theoretically inclined engineers involved in bifurcation theory and its applications to dynamical systems and nonlinear analysis.” (László Hatvani, Acta Scientiarum Mathematicarum (Szeged), Vol. 75 (3-4), 2009)
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- PublisherSpringer
- Publication date2010
- ISBN 10 9048179696
- ISBN 13 9789048179695
- BindingPaperback
- Number of pages270
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Topological Degree Approach to Bifurcation Problems (Topological Fixed Point Theory and Its Applications) by Fekan, Michal [Paperback ]
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Book Description Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 1. 1 Preface Many phenomena from physics, biology, chemistry and economics are modeled by di erential equations with parameters. When a nonlinear equation is est- lished, its behavior/dynamics should be understood. In general, it is impossible to nd a complete dynamics of a nonlinear di erential equation. Hence at least, either periodic or irregular/chaotic solutions are tried to be shown. So a pr- erty of a desired solution of a nonlinear equation is given as a parameterized boundary value problem. Consequently, the task is transformed to a solvability of an abstract nonlinear equation with parameters on a certain functional space. When a family of solutions of the abstract equation is known for some para- ters, the persistence or bifurcations of solutions from that family is studied as parameters are changing. There are several approaches to handle such nonl- ear bifurcation problems. One of them is a topological degree method, which is rather powerful in cases when nonlinearities are not enough smooth. The aim of this book is to present several original bifurcation results achieved by the author using the topological degree theory. The scope of the results is rather broad from showing periodic and chaotic behavior of non-smooth mechanical systems through the existence of traveling waves for ordinary di erential eq- tions on in nite lattices up to study periodic oscillations of undamped abstract waveequationsonHilbertspaceswithapplicationstononlinearbeamandstring partial di erential equations. 1. Seller Inventory # 9789048179695
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Book Description Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Includes (1) Rigorous proofs of chaotic solutions for discontinuous differential equations and differential inclusions (2) Bifurcations of periodic solutions in differential inclusions and systems with relay hysteresis (3) The persistence of traveling wa. Seller Inventory # 5821803
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