TY - JOUR

T1 - Hausdorff and fractal dimension estimates for invariant sets of non-injective maps

AU - Boichenko, V. A.

AU - Franz, A.

AU - Leonov, G. A.

AU - Reitmann, V.

N1 - Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1998

Y1 - 1998

N2 - 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 Hausdorff 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.

AB - 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 Hausdorff 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.

KW - Fractal dimension estimates

KW - Hausdorff dimension estimates

KW - Non-injective maps

KW - Singular values

KW - Tangent map

UR - http://www.scopus.com/inward/record.url?scp=21944432516&partnerID=8YFLogxK

U2 - 10.4171/ZAA/816

DO - 10.4171/ZAA/816

M3 - Article

AN - SCOPUS:21944432516

VL - 17

SP - 207

EP - 223

JO - Zeitschrift fur Analysis und ihre Anwendungen

JF - Zeitschrift fur Analysis und ihre Anwendungen

SN - 0232-2064

IS - 1

ER -