Fr. 178.00

Dimension Theory for Ordinary Differential Equations

English · Paperback / Softback

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Description

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This book is devoted to the estimation of dimension-like characteristics (Hausdorff dimension, fractal dimension, Lyapunov dimension, topological entropy) for attractors
(mainly global B-attractors) of ordinary differential equations, time-discrete systems and dynamical systems on finite-dimensional manifolds. The contraction under flows of
parameter-dependent outer measures is shown by introducing varying Lyapunov functions or metric tensors in the calculation of singular values. For the attractors of the Henon and Lorenz systems, exact formulae for the Lyapunov dimension are derived.

List of contents

Basic facts from matrix theory - Attractors, stability and Lyapunov functions - Introduction to dimension theory - Dimension and Lyapunov functions - Dimension estimates for invariant sets of vector fields on manifolds

About the author

Dr. Vladimir A. Boichenko, Barrikada Company, St. Petersburg

Prof. Dr. Gennadij A. Leonov, St. Petersburg State University

Dr. Volker Reitmann, MPI for the Physics of Complex Systems, Dresden

Report

"Concluding, one may say that the introductory parts of the book are suitable for graduate students, and in the advanced sections even experts in the field will certainly discover novelties."
Zentralblatt Mathematik, 20/2006

Product details

Authors Vladimir Boichenko, Vladimir A Boichenko, Vladimir A. Boichenko, Genadij Leonov, Genadij A Leonov, Genadij A. Leonov, Gennadij A. Leonov, Reitmann, Volker Reitmann
Publisher Vieweg+Teubner
 
Languages English
Product format Paperback / Softback
Released 01.01.2005
 
EAN 9783519004370
ISBN 978-3-519-00437-0
No. of pages 441
Dimensions 172 mm x 238 mm x 26 mm
Weight 752 g
Illustrations 443 p. 4 illus.
Series Teubner-Texte zur Mathematik
Teubner-Texte zur Mathematik
Subjects Natural sciences, medicine, IT, technology > Mathematics > Analysis

Mathematik, Analysis

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