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. IncludesRigorous proofs of chaotic solutions for discontinuous differential equations and differential inclusions Includes bifurcations of periodic solutions in differential inclusions and systems with relay hysteresis The persistence of traveling waves under spatial discretization of sine-Gordon and Klein-Gordon partial differential equations INDICE: 1: Introduction.- 2: Theoretical Background.- 3: Bifurcation of Periodic Solutions.- 4: Bifurcation of Chaotic Solutions.- 5: Topological Transversality.- 6: Travelling Waves on Lattices.- 7: Periodic Oscillations of Wave Equations.- 8: Topological Degree for Wave Equations.- Bibliography.- Index.
- ISBN: 978-1-4020-8723-3
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 270
- Fecha Publicación: 01/07/2008
- Nº Volúmenes: 1
- Idioma: Inglés