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ArticleOriginal scientific text

Title

Transverse Hausdorff dimension of codim-1 C2-foliations

Authors 1, 2

Affiliations

  1. Department of Mathematics and Informatics, Chiba University, Chiba, Japan
  2. Institute of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland

Abstract

The Hausdorff dimension of the holonomy pseudogroup of a codimension-one foliation ℱ is shown to coincide with the Hausdorff dimension of the space of compact leaves (traced on a complete transversal) when ℱ is non-minimal, and to be equal to zero when ℱ is minimal with non-trivial leaf holonomy.

Bibliography

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  2. [Ed] G. A. Edgar, Measure, Topology and Fractal Geometry, Undergrad. Texts in Math., Springer, New York, 1990.
  3. [HH] G. Hector and U. Hirsch, Introduction to the Geometry of Foliations, Part B, Vieweg, Braunschweig, 1983.
  4. [He] M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES 49 (1979), 1-233.
  5. [La] C. Lamoureux, Quelques conditions d'existence de feuilles compactes, Ann. Inst. Fourier (Grenoble) 24 (4) (1974), 229-240.
  6. [Sa] R. Sacksteder, Foliations and pseudogroups, Amer. J. Math. 87 (1965), 79-102.
  7. [Ta] I. Tamura, Topology of Foliations: An Introduction, Amer. Math. Soc., Providence, 1992.
  8. [Wa] P. Walczak, Losing Hausdorff dimension while generating pseudogroups, this issue, 211-237.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm149/fm14934.pdf

Fundamenta Mathematicae
1996/149/3
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Pages:
239-244
Main language of publication
English
Received
1995-02-28
Accepted
1995-10-16
Published
1996
Exact and natural sciences