TY - BOOK AU - Fečkan,Michal ED - SpringerLink (Online service) TI - Topological Degree Approach to Bifurcation Problems T2 - Topological Fixed Point Theory and Its Applications SN - 9781402087240 AV - QA611-614.97 U1 - 514 23 PY - 2008/// CY - Dordrecht PB - Springer Netherlands KW - Mathematics KW - Mathematical analysis KW - Analysis (Mathematics) KW - Dynamics KW - Ergodic theory KW - Topology KW - Mechanics KW - Vibration KW - Dynamical systems KW - Analysis KW - Dynamical Systems and Ergodic Theory KW - Vibration, Dynamical Systems, Control N1 - 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 N2 - 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 UR - http://dx.doi.org/10.1007/978-1-4020-8724-0 ER -