Dimension Theory for Ordinary Differential Equations
Language: English
Published by Walter de Gruyter, Incorporated, 2005
- Softcover
- New
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pp. 443 1st Edition, Reprint.
Seller Inventory # 2648036758
- Title
- Dimension Theory for Ordinary Differential Equations
- Author
- Volker Reitmann Genadij A. Leonov Vladimir A. Boichenko
- Publisher
- Walter de Gruyter, Incorporated
- Publication year
- 2005
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 3519004372
- ISBN 13
- 9783519004370
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.
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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
Prof. Dr. Gennadij A. Leonov, St. Petersburg State University
Dr. Volker Reitmann, MPI for the Physics of Complex Systems, Dresden
"About the title" may belong to another edition of this title.
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