Dimension theory for ordinary differential equations
著者
書誌事項
Dimension theory for ordinary differential equations
（Teubner-Texte zur Mathematik, Bd. 141）
Teubner, c2005
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注記
Literaturverz. S. 415 - 434
内容説明・目次
内容説明
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.
目次
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
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