Geometry of Markov systems and codimension one foliations

Andrzej Biś, and Mariusz Urbański. "Geometry of Markov systems and codimension one foliations." Annales Polonici Mathematici 94.2 (2008): 187-196. <http://eudml.org/doc/280747>.

@article{AndrzejBiś2008,
abstract = {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.},
author = {Andrzej Biś, Mariusz Urbański},
journal = {Annales Polonici Mathematici},
keywords = {codimension 1 foliation; exceptional minimal sets; contracting and parabolic Markov systems; Hausdorff dimension},
language = {eng},
number = {2},
pages = {187-196},
title = {Geometry of Markov systems and codimension one foliations},
url = {http://eudml.org/doc/280747},
volume = {94},
year = {2008},
}

TY - JOUR
AU - Andrzej Biś
AU - Mariusz Urbański
TI - Geometry of Markov systems and codimension one foliations
JO - Annales Polonici Mathematici
PY - 2008
VL - 94
IS - 2
SP - 187
EP - 196
AB - 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.
LA - eng
KW - codimension 1 foliation; exceptional minimal sets; contracting and parabolic Markov systems; Hausdorff dimension
UR - http://eudml.org/doc/280747
ER -