This book deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold. Its main purpose is to present, as completely as possible, the basic results concerning the existence of stable and unstable local manifolds and the recent advancements in the theory of finitely smooth normal forms of vector fields and diffeomorphisms in the vicinity of a rest point and a periodic trajectory. A summary of the results obtained so far in the investigation of dynamical systems near an arbitrary invariant submanifold is also given.
Contents:
- Topological Properties of Flows and Cascades in the Vicinity of a Rest Point and a Periodic Trajectory
- Finitely Smooth Normal Forms of Vector Fields and Diffeomorphisms
- Linear Extensions of Dynamical Systems
- Invariant Subbundles of Weakly Non-Linear Extensions
- Invariant Manifolds
- Normal Forms in the Vicinity of an Invariant Manifold
Readership: Nonlinear scientists and mathematicians.
