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Hausdorff dimension estimates for non-injective maps using the cardinality of the pre-image sets

Astrid Franz

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Recommended by P Gaspard

Upper bounds for the Hausdorff dimension of compact invariant sets of C1-maps on smooth Riemannian manifolds are given in terms of the singular values of the tangent map and the multiplicity function of the map, describing the number of pre-images of a certain point in a given set. For non-injective maps this improves previous results using only the singular values.


PACS

02.30.Cj Measure and integration

02.40.-k Geometry, differential geometry, and topology

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

MSC

28A78 Hausdorff and packing measures

37F35 Conformal densities and Hausdorff dimension

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 5 (September 2000)

Received 22 March 1999, in final form 22 May 2000



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