Vladimir A Boichenko

(Author)

Dimension Theory for Ordinary Differential Equations (Softcover Reprint of the Original 1st 2005)Paperback - Softcover Reprint of the Original 1st 2005, 8 December 2005

Dimension Theory for Ordinary Differential Equations (Softcover Reprint of the Original 1st 2005)
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Part of Series
Teubner-Texte Zur Mathematik
Print Length
443 pages
Language
English
Publisher
Vieweg+teubner Verlag
Date Published
8 Dec 2005
ISBN-10
3519004372
ISBN-13
9783519004370

Description

The book is concerned with upper bounds for the Hausdorff and Fractal dimensions of flow invariant compact sets in Euclidean space and on Riemannian manifolds and the application of such bounds to global stability investigations of equilibrium points. The dimension estimates are formulated in terms of the eigenvalues of the symmetric part of the linearized vector field by including Lyapunov functions into the contraction conditions for outer Hausdorff measures. Various types of local, global and uniform Lyapunov exponents are introduced. On the base of such exponents the Lyapunov dimension of a set is defined and the Kaplan-Yorke formula is discussed. Upper estimates for the topological entropy are derived using Lyapunov functions and adapted Lozinskii norms.

Product Details

Authors:
Vladimir A BoichenkoGenadij A LeonovVolker Reitmann
Book Edition:
Softcover Reprint of the Original 1st 2005
Book Format:
Paperback
Country of Origin:
US
Date Published:
8 December 2005
Dimensions:
24.41 x 16.99 x 2.31 cm
ISBN-10:
3519004372
ISBN-13:
9783519004370
Language:
English
Location:
Wiesbaden
Pages:
443
Weight:
707.6 gm

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