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＜電子ブック＞
Topological Degree Approach to Bifurcation Problems / by Michal Fečkan
(Topological Fixed Point Theory and Its Applications ; 5)

版	1st ed. 2008.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	IX, 261 p. 17 illus : online resource
著者標目	*Fečkan, Michal author SpringerLink (Online service)
件　名	LCSH:Topology LCSH:Mathematical analysis LCSH:Dynamical systems LCSH:Mechanics LCSH:Multibody systems LCSH:Vibration LCSH:Mechanics, Applied FREE:Topology FREE:Analysis FREE:Dynamical Systems FREE:Classical Mechanics FREE:Multibody Systems and Mechanical Vibrations
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-1-4020-8724-0

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