Zeitschrift für Analysis und ihre Anwendungen 22 (2003), No. 3, 553--568
Copyright Heldermann Verlag 2003
Maximum Local Lyapunov Dimension Bounds the Box Dimension. Direct Proof for Invariant Sets on Riemannian Manifolds
Karin Gelfert
Max-Planck-Institut für die, Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany
For a C1 map φ on a Riemannian manifold and for a compact invariant set K it is proven that the maximal local Lyapunov dimension of φ on K bounds the box dimension of K from above. A version for Hilbert spaces is also presented. The introduction of an adapted Riemannian metric provides in a certain sense an optimal upper bound for the box dimension of the Lorenz attractor.
Keywords: Box dimension, Lyapunov dimension, singular value function.
MSC: 37C45; 37L30
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