Displaying similar documents to “Leaves of Markov local minimal sets in foliations of codimension one.”

Geometry of Markov systems and codimension one foliations

Andrzej Biś, Mariusz Urbański (2008)

Annales Polonici Mathematici

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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.

Smoothability of proper foliations

John Cantwell, Lawrence Conlon (1988)

Annales de l'institut Fourier

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Compact, C 2 -foliated manifolds of codimension one, having all leaves proper, are shown to be C -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class C . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class C r and of class C r + 1 for every nonnegative integer r .

Foliations with all leaves compact

D. B. A. Epstein (1976)

Annales de l'institut Fourier

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The notion of the “volume" of a leaf in a foliated space is defined. If L is a compact leaf, then any leaf entering a small neighbourhood of L either has a very large volume, or a volume which is approximatively an integral multiple of the volume of L . If all leaves are compact there are three related objects to study. Firstly the topology of the quotient space obtained by identifying each leaf to a point ; secondly the holonomy of a leaf ; and thirdly whether the leaves have a locally...

Limit sets of foliations

Richard Sacksteder, Art J. Schwartz (1965)

Annales de l'institut Fourier

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Soit V une variété munie d’une structure feuilletée de co-dimension un. On démontre plusieurs théorème relatifs à des conditions entraînant que le groupe d’holonomie et le pseudo-groupe d’holonomie d’une certaine feuille F V est infini.