JournalszaaVol. 17, No. 1pp. 207–223

Hausdorff and Fractal Dimension Estimates for Invariant Sets of Non-Injective Maps

  • V.A. Boichenko

    St. Petersburg State University, Russian Federation
  • A. Franz

    Technische Universität Dresden, Germany
  • G.A. Leonov

    St. Petersburg State University, Russian Federation
  • Volker Reitmann

    Technische Universität Dresden, Germany
Hausdorff and Fractal Dimension Estimates for Invariant Sets of Non-Injective Maps cover
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Abstract

In this paper we are concerned with upper bounds for the Hausdorff and fractal dimensions of negatively invariant sets of maps on Riemannian manifolds. We consider a special class of non-injective maps, for which we introduce a factor describing the "degree of non-injectivity". This factor can be included in the Hausdorif dimension estimates of Douady-Oesterlé type [2, 7, 10] and in fractal dimension estimates [5, 13, 15] in order to weaken the condition to the singular values of the tangent map. In a number of cases we get better upper dimension estimates.

Cite this article

V.A. Boichenko, A. Franz, G.A. Leonov, Volker Reitmann, Hausdorff and Fractal Dimension Estimates for Invariant Sets of Non-Injective Maps. Z. Anal. Anwend. 17 (1998), no. 1, pp. 207–223

DOI 10.4171/ZAA/816