This book is devoted to bifurcations of periodic, subharmonic and chaotic oscillations, and travelling waves in nonlinear differential equations and discrete dynamical systems by using the topological degree theory both for single-valued and multi-valued mappings in Banach spaces. Original bifurcation results are proved with applications to a broad variety of nonlinear problems ranging from non-smooth and discontinuous mechanical systems, weakly coupled oscillators, systems with relay hysteresis, through infinite chains of differential equations on lattices, to string and beam partial differential equations. Next, the chaotic behaviour is also investigated for maps possessing topologically transversally intersecting invariant manifolds. This book is intended for post-graduate students and researchers with an interest in applications of topological bifurcation methods to dynamical systems and non-linear analysis, in particular to differential equations and inclusions, and maps.Let us note that periodic and almost periodic solutions to dry friction problems are also investigated in [50, 59-63]. The numerical analysis is given in [12, 164, 165] for a mechanical model of a friction oscillator with simultaneous self and external anbsp;...
|Title||:||Topological Degree Approach to Bifurcation Problems|
|Publisher||:||Springer Science & Business Media - 2008-06-29|