By Kaspar Nipp, Daniel Stoffer
During this booklet, dynamical platforms are investigated from a geometrical point of view. Admitting an invariant manifold is a sturdy geometric estate of a dynamical method. this article offers rigorous effects on invariant manifolds and provides examples of attainable purposes. within the first half, discrete dynamical structures in Banach areas are thought of. effects at the lifestyles and smoothness of appealing and repulsive invariant manifolds are derived. moreover, perturbations and approximations of the manifolds and the foliation of the adjoining area are taken care of. within the moment half, analogous effects for non-stop dynamical structures in finite dimensions are validated. within the 3rd half, the speculation constructed is utilized to difficulties in numerical research and to singularly perturbed platforms of normal differential equations. The mathematical method relies at the so-called graph remodel, already utilized by Hadamard in 1901. the purpose is to set up invariant manifold leads to an easy environment that offers quantitative estimates. The e-book is concentrated at researchers within the box of dynamical structures attracted to distinctive theorems which are effortless to use. the applying half may additionally function an underlying textual content for a scholar seminar in arithmetic. A book of the ecu Mathematical Society (EMS). dispensed in the Americas via the yankee Mathematical Society.