TY - BOOK ID - 4804148 TI - Topological degree approach to bifurcation problems PY - 2008 SN - 9781402087240 1402087233 9781402087233 9048179696 9786611491048 1281491047 1402087241 PB - [New York] : Springer, DB - UniCat KW - Mathematics. KW - Analysis. KW - Topology. KW - Dynamical Systems and Ergodic Theory. KW - Mechanics. KW - Vibration, Dynamical Systems, Control. KW - Global analysis (Mathematics). KW - Differentiable dynamical systems. KW - Vibration. KW - Mathématiques KW - Analyse globale (Mathématiques) KW - Dynamique différentiable KW - Topologie KW - Mécanique KW - Vibration KW - Bifurcation theory. KW - Bifurcation theory KW - Topology KW - Mathematics KW - Engineering & Applied Sciences KW - Physical Sciences & Mathematics KW - Applied Mathematics KW - Calculus KW - Analysis situs KW - Position analysis KW - Rubber-sheet geometry KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Dynamics. KW - Ergodic theory. KW - Dynamical systems. KW - Geometry KW - Polyhedra KW - Set theory KW - Algebras, Linear KW - Differential equations, Nonlinear KW - Stability KW - Numerical solutions KW - Classical Mechanics. KW - Cycles KW - Mechanics KW - Sound KW - Classical mechanics KW - Newtonian mechanics KW - Physics KW - Dynamics KW - Quantum theory KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Differential equations KW - Global analysis (Mathematics) KW - Topological dynamics KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Statics KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - 517.1 Mathematical analysis KW - Mathematical analysis KW - Calculus. KW - Analysis (Mathematics) KW - Fluxions (Mathematics) KW - Infinitesimal calculus KW - Limits (Mathematics) KW - Functions KW - Geometry, Infinitesimal UR - https://www.unicat.be/uniCat?func=search&query=sysid:4804148 AB - 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. ER -