Dimension Theory for Ordinary Differential Equations [Paperback]

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.
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 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, 20/2006Modern Topics in Applied Analysis and Dynamical SystemsDr. 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, DresdenThis 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.
Moderne Methoden f?r die Dimensionstheorie l£)