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Topological Degree Approach to Bifurcation Problems

By: Fečkan, Michal [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Topological Fixed Point Theory and Its Applications: 5Publisher: Dordrecht : Springer Netherlands, 2008.Description: IX, 261 p. 17 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781402087240.Subject(s): Mathematics | Mathematical analysis | Analysis (Mathematics) | Dynamics | Ergodic theory | Topology | Mechanics | Vibration | Dynamical systems | Mathematics | Topology | Analysis | Dynamical Systems and Ergodic Theory | Mechanics | Vibration, Dynamical Systems, ControlDDC classification: 514 Online resources: Click here to access online
Contents:
Theoretical Background -- Bifurcation of Periodic Solutions -- Bifurcation of Chaotic Solutions -- Topological Transversality -- Traveling Waves on Lattices -- Periodic Oscillations of Wave Equations -- Topological Degree for Wave Equations.
In: Springer eBooksSummary: 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.
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E books E books PK Kelkar Library, IIT Kanpur
Available EBK10342
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Theoretical Background -- Bifurcation of Periodic Solutions -- Bifurcation of Chaotic Solutions -- Topological Transversality -- Traveling Waves on Lattices -- Periodic Oscillations of Wave Equations -- Topological Degree for Wave Equations.

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.

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