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Topological Degree Approach to Bifurcation Problems - Michal Feckan
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Michal Feckan:
Topological Degree Approach to Bifurcation Problems - gebunden oder broschiert

ISBN: 1402087233

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[EAN: 9781402087233], Neubuch, [PU: Springer], MICHAL FECKAN,MECHANICS,MECHANICAL ENGINEERING,MATHEMATICS, Mathematics|Mathematical Analysis, Mathematics|Topology, Hardcover. 261 pages. Dimensions: 9.4in. x 6.3in. x 0.8in.1. 1 Preface Many phenomena from physics, biology, chemistry and economics are modeled by dierential equations with parameters. When a nonlinear equation is est- lished, its behaviordynamics should be understood. In general, it is impossible to nd a complete dynamics of a nonlinear dierential equation. Hence at least, either periodic or irregularchaotic 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 dierential eq- tions on innite lattices up to study periodic oscillations of undamped abstract waveequationsonHilbertspaceswithapplicationstononlinearbeamandstring partial dierential equations. 1. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN.

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Topological Degree Approach to Bifurcation Problems (Hardback) - Michal Feckan
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2008, ISBN: 1402087233

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[EAN: 9781402087233], Neubuch, [PU: Springer-Verlag New York Inc., United States], Mathematics|Mathematical Analysis, Mathematics|Topology, Language: English . Brand New Book ***** Print on Demand *****. 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.

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Topological Degree Approach to Bifurcation Problems (Hardback) - Michal Feckan
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Michal Feckan:
Topological Degree Approach to Bifurcation Problems (Hardback) - gebunden oder broschiert

2008, ISBN: 1402087233

ID: 4742139123

[EAN: 9781402087233], Neubuch, [PU: Springer-Verlag New York Inc., United States], Mathematics|Mathematical Analysis, Mathematics|Topology, Language: English . Brand New Book ***** Print on Demand *****.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.

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Topological Degree Approach to Bifurcation Problems - Michal Feckan
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Topological Degree Approach to Bifurcation Problems - neues Buch

ISBN: 9781402087233

ID: 978140208723

This book is devoted to bifurcations of periodic, subharmonic and chaotic oscillations, and travelling waves in nonlinear differential equations and discrete dynamical systems by using the topological degree theory both for single-valued and multi-valued mappings in Banach spaces. Original bifurcation results are proved with applications to a broad variety of nonlinear problems ranging from non-smooth and discontinuous mechanical systems, weakly coupled oscillators, systems with relay hysteresis, through infinite chains of differential equations on lattices involving also spatially discretized partial differential equations, and to string and beam partial differential equations. Next, the chaotic behaviour is also investigated for maps possessing topologically transversally intersecting invariant manifolds. Moreover, periodic orbits with arbitrarily high periods, the so-called blue sky catastrophe, are shown for reversible differential systems and maps. Finally, bifurcations of large amplitude oscillations for discontinuous undamped wave partial differential equations are given as well.This book is mainly intended for post-graduate students and researchers in mathematics with an interest in applications of topological bifurcation methods to dynamical systems and nonlinear analysis, in particular to differential equations and inclusions, and maps. But, among others, it could also be used either by physicists studying oscillations of nonlinear mechanical systems or by engineers investigating vibrations of strings and beams, and electrical circuits. Michal Feckan, Books, Science and Nature, Topological Degree Approach to Bifurcation Problems Books>Science and Nature, Springer Netherlands

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Topological Degree Approach to Bifurcation Problems - Michal Feckan
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Topological Degree Approach to Bifurcation Problems - gebunden oder broschiert

2008, ISBN: 9781402087233

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Details zum Buch
Topological Degree Approach to Bifurcation Problems
Autor:

Feckan, Michal

Titel:

Topological Degree Approach to Bifurcation Problems

ISBN-Nummer:

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; 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 make this book valuable to both the applied sciences and mathematical fields, ensuring the book should also be of interest to physicists and theoretically inclined engineers interested in bifurcation theory and its applications to dynamical systems and nonlinear analysis.

Detailangaben zum Buch - Topological Degree Approach to Bifurcation Problems


EAN (ISBN-13): 9781402087233
ISBN (ISBN-10): 1402087233
Gebundene Ausgabe
Erscheinungsjahr: 2008
Herausgeber: SPRINGER VERLAG GMBH
261 Seiten
Gewicht: 0,522 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 12.07.2007 19:01:16
Buch zuletzt gefunden am 21.02.2017 06:21:41
ISBN/EAN: 9781402087233

ISBN - alternative Schreibweisen:
1-4020-8723-3, 978-1-4020-8723-3


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