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

Vladimir A. Boichenko | Zendy; Alfred M. Franz | Zendy; Г. А. Леонов | Zendy; Volker Reitmann | Zendy

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

Author(s) -

Vladimir A. Boichenko,

Alfred M. Franz,

Г. А. Леонов,

Volker Reitmann

Publication year - 1998

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/816

Subject(s) - injective function , hausdorff dimension , invariant (physics) , mathematics , fractal , pure mathematics , fractal dimension , minkowski–bouligand dimension , packing dimension , effective dimension , hausdorff space , box counting , fractal analysis , mathematical analysis , mathematical physics

In this paper we are concerned with upper bounds for the Hausdorif 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 DouadyOesterlé 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.

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