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Flots topologiquement transitifs sur les surfaces compactes sans bord: contrexemples à une conjecture de Katok

Published online by Cambridge University Press:  19 September 2008

Gilbert Levitt
Affiliation:
Département de Mathématiques, Université Paris VII, 2 Place Jussieu, 75251 Paris, Cedex 05, France
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Abstract

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We prove that on closed surfaces of higher genus cohomological invariants are not sufficient to distinguish topologically transitive flows which are not topologically conjugate; this contradicts a conjecture of Katok.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1983

References

RÉFÉRENCES

[1]Fathi, A., Laudenbach, F. & Poenaru, V.. Travaux de Thurston sur les surfaces. Astérisque. 66–67 (1979).Google Scholar
[2]Fried, D.. Geometry of cross-sections to flows. Topology 21 (1981), 353371.CrossRefGoogle Scholar
[3]Katok, A. B.. Invariant measures of flows on oriented surfaces. Soviet Math. Dokl. 14 (1973) (4), 11041108.Google Scholar
[4]Keane, M. & Rauzy, G.. Stride ergodicité des échanges d'intervalles, Math. Z. 174 (1980), 203212.CrossRefGoogle Scholar
[5]Levitt, G.. Pantalons et feuilletages des surfaces. Topology. 21 (1982), 933.CrossRefGoogle Scholar
[6]Levitt, G.. La décomposition dynamique et la différentiabilité des feuilletages des surfaces. Preprint.Google Scholar
[7]Masur, H.. Interval exchange transformations and measured foliations. Preprint.Google Scholar
[8]Moser, J.. On the volume elements on a manifold. Trans. Amer. Math. Soc. 120 (1965), 286294.CrossRefGoogle Scholar
[9]Rees, M.. An alternative approach to the ergodic theory of measured foliations on surfaces. Ergod. Th. & Dynam. Sys. 1 (1981), 461488.CrossRefGoogle Scholar
[10]Schwartzman, S.. Asymptotic cycles. Ann. of Math. 66 (1957), 270284.CrossRefGoogle Scholar
[11]Sullivan, D.. Cycles for the dynamical study of foliated manifolds and complex manifolds. Invent. Math. 36 (1976), 225255.CrossRefGoogle Scholar
[12]Thurston, W. P.. On the geometry and dynamics of diffeomorphisms of surfaces, I. Preprint: Princeton University.Google Scholar
[13]Veech, W. A.. Quasiminimal invariants for foliations of orientable closed surfaces. Preprint. Rice University.Google Scholar
[14]Veech, W. A., Gauss measures for transformations on the space of interval exchange maps. Ann. of Math. 115 (1982), 201242.CrossRefGoogle Scholar