Hausdorff and Fractal Dimension Estimates for Invariant Sets of Non-Injective Maps
Hausdorff and Fractal Dimension Estimates for Invariant Sets of Non-Injective Maps
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DOI：
10.4171/zaa/816
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发表时间：
1998-03
影响因子：
1.2
通讯作者：
V. Boichenko;A. Franz;G. Leonov;V. Reitmann
中科院分区：
文献类型：
--
作者：
V. Boichenko;A. Franz;G. Leonov;V. Reitmann
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.
