Losing Hausdorff dimension while generating pseudogroups

Walczak, Paweł

Walczak, Paweł

Fundamenta Mathematicae, Tome 149 (1996), p. 211-237 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $d i m_{H} G$ of G. Since $d i m_{H} G \leq d i m_{H} X$ , the dimension loss $d l_{H} G = d i m_{H} X - d i m_{H} G$ can be considered as a “topological price” one has to pay to generate G. We collect some properties of $d i m_{H}$ and $d l_{H}$ (for example, both of them are invariant under Lipschitz isomorphisms of pseudogroups) and we either estimate or calculate $d i m_{H} G$ for pseudogroups arising from classical dynamical systems, group actions, foliations, etc.

Publié le : 1996-01-01

Zbl 0861.54033

EUDML-ID : urn:eudml:doc:212120

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     author = {Pawe\l\ Walczak},
     title = {Losing Hausdorff dimension while generating pseudogroups},
     journal = {Fundamenta Mathematicae},
     volume = {149},
     year = {1996},
     pages = {211-237},
     zbl = {0861.54033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv149i3p211bwm}
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Walczak, Paweł. Losing Hausdorff dimension while generating pseudogroups. Fundamenta Mathematicae, Tome 149 (1996) pp. 211-237. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i3p211bwm/

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