Hausdorff Dimension of Non-Hyperbolic Repellers. I: Maps with Holes

被引：0

作者：

Vanderlei Horita

Marcelo Viana

机构：

[1] IBILCE/UNESP,Departamento de Matemática

[2] IMPA,undefined

来源：

Journal of Statistical Physics | 2001年 / 105卷

关键词：

Hausdorff dimension; non-uniform hyperbolicity; repeller; dynamical dimension;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

引用

页码：835 / 862

页数：27

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[7]

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[8]

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