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Invariant Manifolds in Discrete and Continuous Dynamical Systems
EMS Tracts in Mathematics Vol. 21

Kaspar Nipp (ETH Zürich, Switzerland)
Daniel Stoffer (ETH Zürich, Switzerland)

Invariant Manifolds in Discrete and Continuous Dynamical Systems

ISBN print 978-3-03719-124-8, ISBN online 978-3-03719-624-3
DOI 10.4171/124
August 2013, 225 pages, hardcover, 17 x 24 cm.
58.00 Euro

In this book dynamical systems are investigated from a geometric viewpoint. Admitting an invariant manifold is a strong geometric property of a dynamical system. This text presents rigorous results on invariant manifolds and gives examples of possible applications.

In the first part discrete dynamical systems in Banach spaces are considered. Results on the existence and smoothness of attractive and repulsive invariant manifolds are derived. In addition, perturbations and approximations of the manifolds and the foliation of the adjacent space are treated. In the second part analogous results for continuous dynamical systems in finite dimensions are established. In the third part the theory developed is applied to problems in numerical analysis and to singularly perturbed systems of ordinary differential equations.

The mathematical approach is based on the so-called graph transform, already used by Hadamard in 1901. The aim is to establish invariant manifold results in a simple setting providing quantitative estimates.

The book is targeted at researchers in the field of dynamical systems interested in precise theorems easy to apply. The application part might also serve as an underlying text for a student seminar in mathematics.

Keywords: Discrete and continuous dynamical systems, invariant manifolds, foliation, singular perturbations, geometric numerical integration, differential algebraic equations

Further Information

Review zbMATH 1291.37004

Review in MR 3098463