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Topological Degree Approach to Bifurcation Problems - pocketboek

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Topological Degree Approach to Bifurcation Problems
auteur:
Titel:
ISBN:

9789048179695


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.

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EAN (ISBN-13): 9789048179695
ISBN (ISBN-10): 9048179696
Gebonden uitgave
pocket book
Verschijningsjaar: 2010
Uitgever: Springer-Verlag GmbH
272 Bladzijden
Gewicht: 0,415 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2011-05-18T11:43:06+02:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2019-12-21T16:40:52+01:00 (Amsterdam)
ISBN/EAN: 9789048179695

ISBN - alternatieve schrijfwijzen:
90-481-7969-6, 978-90-481-7969-5
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: michal
Titel van het boek: bifurcation, approach problems, bifur, the second degree, fixed point theory and applications

Gegevens van de uitgever

Auteur: Michal Fečkan
Titel: Topological Fixed Point Theory and Its Applications; Topological Degree Approach to Bifurcation Problems
Uitgeverij: Springer; Springer Netherland
261 Bladzijden
Verschijningsjaar: 2010-11-30
Dordrecht; NL
Gedrukt / Gemaakt in
Gewicht: 0,454 kg
Taal: Engels
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
POD
IX, 261 p. 17 illus.

BC; Topology; Hardcover, Softcover / Mathematik/Geometrie; Topologie; Verstehen; Boundary value problem; Topology; Vibration; calculus; differential topology; friction; partial differential equation; wave equation; Analysis; Dynamical Systems and Ergodic Theory; Classical Mechanics; Vibration, Dynamical Systems, Control; Topology; Analysis; Dynamical Systems; Classical Mechanics; Multibody Systems and Mechanical Vibrations; Mathematische Analysis, allgemein; Kybernetik und Systemtheorie; Klassische Mechanik; Maschinenbau: Festkörpermechanik; BB

1. Introduction 1.1. Preface 1.2. An Illustrative Perturbed Problem 1.3. A Brief Summary of the Book 2. Theoretical Background 2.1. Linear Functional Analysis 2.2. Nonlinear Functional Analysis 2.2.1. Implicit Function Theorem 2.2.2. Lyapunov-Schmidt Method 2.2.3. Leray-Schauder Degree 2.3. Differential Topology 2.3.1. Differentiable Manifolds 2.3.2. Symplectic Surfaces 2.3.3. Intersection Numbers of Manifolds 2.3.4. Brouwer Degree on Manifolds 2.3.5. Vector Bundles 2.3.6. Euler Characteristic 2.4. Multivalued Mappings 2.4.1. Upper Semicontinuity 2.4.2. Measurable Selections 2.4.3. Degree Theory for Set-Valued Maps 2.5. Dynamical Systems 2.5.1. Exponential Dichotomies 2.5.2. Chaos in Discrete Dynamical Systems 2.5.3. Periodic O.D.Eqns 2.5.4. Vector Fields 2.6. Center Manifolds For Infinite Dimensions 3. Bifurcation of Periodic Solutions 3.1. Bifurcation of Periodics from Homoclinics I 3.1.1. Discontinuous O.D.Eqns 3.1.2. The Linearized Equation 3.1.3. Subharmonics for Regular Periodic Perturbations 3.1.4. Subharmonics for Singular Periodic Perturbations 3.1.5. Subharmonics for Regular Autonomous Perturbations 3.1.6. Applications to Discontinuous O.D.Eqns 3.1.7. Bounded Solutions Close to Homoclinics 3.2. Bifurcation of Periodics from Homoclinics II 3.2.1. Singular Discontinuous O.D.Eqns 3.2.2. Linearized Equations 3.2.3. Bifurcation of Subharmonics 3.2.4. Applications to Singular Discontinuous O.D.Eqns 3.3. Bifurcation of Periodics from Periodics 3.3.1. Discontinuous O.D.Eqns 3.3.2. Linearized Problem 3.3.3. Bifurcation of Periodics in Nonautonomous Systems 3.3.4. Bifurcation of Periodics in Autonomous Systems 3.3.5. Applications to Discontinuous O.D.Eqns 3.3.6. Concluding Remarks 3.4. Bifurcation of Periodics in Relay Systems 3.4.1. Systems with Relay Hysteresis 3.4.2. Bifurcation of Periodics 3.4.3. Third-Order O.D.Eqns with Small Relay Hysteresis 3.5. Nonlinear Oscillators with Weak Couplings 3.5.1. Weakly Coupled Systems 3.5.2. Forced Oscillations from Single Periodics 3.5.3. Forced Oscillations from Families of Periodics 3.5.4. Applications to Weakly Coupled Nonlinear Oscillators 4. Bifurcation of Chaotic Solutions 4.1. Chaotic Differential Inclusions 4.1.1. Nonautonomous Discontinuous O.D.Eqns 4.1.2. The Linearized equation 4.1.3. Bifurcation of Chaotic Solutions 4.1.4. Chaos from Homoclinic Manifolds 4.1.5. Almost and Quasi Periodic Discontinuous O.D.Eqns 4.2. Chaos in Periodic Differential Inclusions 4.2.1. Regular Periodic Perturbations 4.2.2. Singular Differential Inclusions 4.3. More about Homoclinic Bifurcations 4.3.1. Transversal Homoclinic Crossing Discontinuity 4.3.2. Homoclinic Sliding on Discontinuity 5. Topological Transversality 5.1. Topological Transversality and Chaos 5.1.1. Topologically Transversal Invariant Sets 5.1.2. Difference Boundary Value Problems 5.1.3. Chaotic Orbits 5.1.4. Periodic Points and Extensions on Invariant Compact Subsets 5.1.5. Perturbed Topological Transversality 5.2. Topological Transversality and Reversibility 5.2.1. Period Blow-up 5.2.2. Period Blow-up for Reversible Diffeomorphisms 5.2.3. Perturbed Period Blow-up 5.2.4. Perturbed Second Order O.D.Eqns 5.3. Chains of Reversible Oscillators 5.3.1. Homoclinic Period Blow-up for Breathers 5.
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