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Group theory --- Symmetry groups --- Groupes, Théorie des --- Groupes symétriques --- Differential equations --- Evolution equations --- Stability. --- Bifurcation theory. --- Numerical solutions. --- Groepen (wiskunde) --- 512.54 --- Groups. Group theory --- 512.54 Groups. Group theory --- Théorie des groupes --- Théorie des groupes --- Groupes symétriques --- Bifurcation theory --- Stability --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Numerical analysis --- 517.91 Differential equations --- Differential equations, Nonlinear --- Numerical solutions --- 517.91 --- Numerical solutions&delete& --- Groupes, Théorie des --- Groupes de symétrie --- Geometrie classique --- Groupes (algebre) --- Groupes de permutations

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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.

Mathematics. --- Analysis. --- Topology. --- Dynamical Systems and Ergodic Theory. --- Mechanics. --- Vibration, Dynamical Systems, Control. --- Global analysis (Mathematics). --- Differentiable dynamical systems. --- Vibration. --- Mathématiques --- Analyse globale (Mathématiques) --- Dynamique différentiable --- Topologie --- Mécanique --- Vibration --- Bifurcation theory. --- Bifurcation theory --- Topology --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Mathematical analysis. --- Analysis (Mathematics). --- Dynamics. --- Ergodic theory. --- Dynamical systems. --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Differential equations, Nonlinear --- Stability --- Numerical solutions --- Classical Mechanics. --- Cycles --- Mechanics --- Sound --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- 517.1 Mathematical analysis --- Mathematical analysis --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal