Geometry of Markov systems and codimension one foliations
Volume 94 / 2008
Annales Polonici Mathematici 94 (2008), 187-196
MSC: Primary 57R30; Secondary 37C45, 37E05, 28A78, 28A80.
DOI: 10.4064/ap94-2-5
Abstract
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.
