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Invariant Manifolds in Discrete and Continuous Dynamical Systems:

Kaspar Nipp ETH Zürich, Switzerland
Daniel Stoffer ETH Zürich, Switzerland
A publication of European Mathematical Society
Available Formats:
Hardcover ISBN: 978-3-03719-124-8
Product Code: EMSTM/21
List Price: $78.00 AMS Member Price:$62.40
Please note AMS points can not be used for this product
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Invariant Manifolds in Discrete and Continuous Dynamical Systems:
Kaspar Nipp ETH Zürich, Switzerland
Daniel Stoffer ETH Zürich, Switzerland
A publication of European Mathematical Society
Available Formats:
 Hardcover ISBN: 978-3-03719-124-8 Product Code: EMSTM/21
 List Price: $78.00 AMS Member Price:$62.40
Please note AMS points can not be used for this product
• Book Details

EMS Tracts in Mathematics
Volume: 212013; 225 pp
MSC: Primary 37; 35; 34; 65;

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 that provides quantitative estimates.

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

Researchers interested in dynamical systems.

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 212013; 225 pp
MSC: Primary 37; 35; 34; 65;

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 that provides quantitative estimates.

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