Measure preserving pseudo-groups and a theorem of Sacksteder

Joseph F. Plante

Annales de l'institut Fourier (1975)

  • Volume: 25, Issue: 1, page 237-249
  • ISSN: 0373-0956

Abstract

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This note is based on a theorem of Sacksteder which generalizes a classical result of Denjoy. Using this theorem and results on the existence of invariant measures, new results are obtained concerning minimal sets for groups of diffeomorphisms of the circle and for foliations of codimension one.

How to cite

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Plante, Joseph F.. "Measure preserving pseudo-groups and a theorem of Sacksteder." Annales de l'institut Fourier 25.1 (1975): 237-249. <http://eudml.org/doc/74212>.

@article{Plante1975,
abstract = {This note is based on a theorem of Sacksteder which generalizes a classical result of Denjoy. Using this theorem and results on the existence of invariant measures, new results are obtained concerning minimal sets for groups of diffeomorphisms of the circle and for foliations of codimension one.},
author = {Plante, Joseph F.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {237-249},
publisher = {Association des Annales de l'Institut Fourier},
title = {Measure preserving pseudo-groups and a theorem of Sacksteder},
url = {http://eudml.org/doc/74212},
volume = {25},
year = {1975},
}

TY - JOUR
AU - Plante, Joseph F.
TI - Measure preserving pseudo-groups and a theorem of Sacksteder
JO - Annales de l'institut Fourier
PY - 1975
PB - Association des Annales de l'Institut Fourier
VL - 25
IS - 1
SP - 237
EP - 249
AB - This note is based on a theorem of Sacksteder which generalizes a classical result of Denjoy. Using this theorem and results on the existence of invariant measures, new results are obtained concerning minimal sets for groups of diffeomorphisms of the circle and for foliations of codimension one.
LA - eng
UR - http://eudml.org/doc/74212
ER -

References

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  1. [1] F. GREENLEAF, Invariant means on topological groups, Van Nostrand, New York (1969). Zbl0174.19001MR40 #4776
  2. [2] M. HIRSCH, W. THURSTON, Foliated bundles, flat manifolds and invariant measures, Annals of Math., (to appear). Zbl0321.57015
  3. [3] R. MOUSSU, F. PELLETIER, Sur le théorème de Poincaré-Bendixson, Annales de l'Institut Fourier, 24 (1974), 131-148. Zbl0273.57008MR50 #11266
  4. [4] V. NEMYTSKII, V. STEPANOV, Qualitative theory of differential equations, Princeton University Press (1960). Zbl0089.29502MR22 #12258
  5. [5] J. PLANTE, A generalization of the Poincaré-Bendixson theorem for foliations of codimension one, Topology, 12 (1973), 177-181. Zbl0254.57014MR49 #6253
  6. [6] J. PLANTE, On the existence of exceptional minimal sets in foliations of codimension one, J. Differential Equations, 15 (1974), 178-194. Zbl0294.57017MR49 #11539
  7. [7] R. SACKSTEDER, Foliations and pseudgroups, American J. of Math., 87 (1965), 79-102. Zbl0136.20903MR30 #4268
  8. [8] R. SACKSTEDER, Groups and pseudogroups acting on S1 and R1, Mimeograph notes, Columbia University. 
  9. [9] J. WOLF, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geometry, 2 (1968), 421-446. Zbl0207.51803MR40 #1939

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