Geometry of Markov systems and codimension one foliations

• Autorzy: Andrzej Biś , Mariusz Urbański
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57R30: Foliations; geometric theory
• 37C45: Dimension theory of dynamical systems
• 28A78: Hausdorff and packing measures
• 28A80: Fractals
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 94
• Numer: 2
• Strony: 187-196

Daty

wydano

2008

Twórcy

autor

Andrzej Biś

• Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

autor

Mariusz Urbański

• Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, U.S.A.

Identyfikatory

DOI

10.4064/ap94-2-5