JournalszaaVol. 22, No. 3pp. 553–568

Maximum Local Lyapunov Dimension Bounds the Box Dimension. Direct Proof for Invariant Sets on Riemannian Manifolds

  • Karin Gelfert

    Physik komplexer Systeme, Dresden, Germany
Maximum Local Lyapunov Dimension Bounds the Box Dimension. Direct Proof for Invariant Sets on Riemannian Manifolds cover
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Abstract

For a C^1 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.

Cite this article

Karin Gelfert, Maximum Local Lyapunov Dimension Bounds the Box Dimension. Direct Proof for Invariant Sets on Riemannian Manifolds. Z. Anal. Anwend. 22 (2003), no. 3, pp. 553–568

DOI 10.4171/ZAA/1162