Dimension theory for ordinary differential equations
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Více o knize
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.
Nákup knihy
Dimension theory for ordinary differential equations, Vladimir A. Bojčenko
- Jazyk
- Rok vydání
- 2005
Doručení
Platební metody
2021 2022 2023
Navrhnout úpravu
- Titul
- Dimension theory for ordinary differential equations
- Jazyk
- anglicky
- Autoři
- Vladimir A. Bojčenko
- Vydavatel
- Teubner
- Rok vydání
- 2005
- ISBN10
- 3519004372
- ISBN13
- 9783519004370
- Série
- Teubner-Texte zur Mathematik
- Kategorie
- Matematika
- Anotace
- 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.