We show that the theory of graph directed Markov systems can be used to study exceptional minimal sets of some foliated manifolds. A C¹ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-5,
author = {Andrzej Bi\'s and Mariusz Urba\'nski},
title = {Geometry of Markov systems and codimension one foliations},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {187-196},
zbl = {1153.57024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-5}
}
Andrzej Biś; Mariusz Urbański. Geometry of Markov systems and codimension one foliations. Annales Polonici Mathematici, Tome 93 (2008) pp. 187-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-2-5/