- Tytuł:
- Losing Hausdorff dimension while generating pseudogroups
- Autorzy:
- Walczak, Paweł
- Powiązania:
- https://bibliotekanauki.pl/articles/1205505.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- 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 $dim_H G$ of G. Since $dim_H G ≤ dim_H X$, the dimension loss $dl_HG = dim_HX - dim_H G$ can be considered as a "topological price" one has to pay to generate G. We collect some properties of $dim_H$ and $dl_H$ (for example, both of them are invariant under Lipschitz isomorphisms of pseudogroups) and we either estimate or calculate $dim_HG$ for pseudogroups arising from classical dynamical systems, group actions, foliations, etc.
- Źródło:
-
Fundamenta Mathematicae; 1996, 149, 3; 211-237
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł