Geometry of Markov systems and codimension one foliations

Volume 94 / 2008

Andrzej Bi/s, Mariusz Urba/nski Annales Polonici Mathematici 94 (2008), 187-196 MSC: Primary 57R30; Secondary 37C45, 37E05, 28A78, 28A80. DOI: 10.4064/ap94-2-5


We show that the theory of graph directed Markov systems can be used to study exceptional minimal sets of some foliated manifolds. A $C^1$ smooth embedding of a contracting or parabolic Markov system into the holonomy pseudogroup of a codimension one foliation allows us to describe in detail the $h$-dimensional Hausdorff and packing measures of the intersection of a complete transversal with exceptional minimal sets.


  • Andrzej Bi/sFaculty of Mathematics and Computer Science
    University of /L/od/x
    Banacha 22
    90-238 /L/od/x, Poland
  • Mariusz Urba/nskiDepartment of Mathematics
    University of North Texas
    P.O. Box 311430
    Denton, TX 76203-1430, U.S.A.

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