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Title

Losing Hausdorff dimension while generating pseudogroups

Authors 1

Affiliations

  1. Institute of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland

Abstract

Considering different finite sets of maps generating a pseudogroup G of locally Lipschitz homeomorphisms between open subsets of a compact metric space X we arrive at a notion of a Hausdorff dimension dimHG of G. Since dimHG≤dimHX, the dimension loss dlHG=dimHX-dimHG can be considered as a "topological price" one has to pay to generate G. We collect some properties of dimH and dlH (for example, both of them are invariant under Lipschitz isomorphisms of pseudogroups) and we either estimate or calculate dimHG for pseudogroups arising from classical dynamical systems, group actions, foliations, etc.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm149/fm14933.pdf

Fundamenta Mathematicae
1996/149/3
Export to PBN, Opens in new tab
Pages:
211-237
Main language of publication
English
Received
1995-02-28
Accepted
1995-10-16
Published
1996
Exact and natural sciences