A spectral-like decomposition for transitive Anosov flows in dimension three

Abstract : Given a (transitive or non-transitive) Anosov vector field X on a closed three dimensional manifold M, one may try to decompose (M, X) by cutting M along tori and Klein bottles transverse to X. We prove that one can find a finite collection of pairwise disjoint, pairwise non-parallel tori and Klein bottles transverse to X, such that the maximal invariant sets of the connected components of satisfy the following properties:each is a compact invariant locally maximal transitive set for X; the collection is canonically attached to the pair (M, X) (i.e. it can be defined independently of the collection of tori and Klein bottles ); the 's are the smallest possible: for every (possibly infinite) collection of tori and Klein bottles transverse to X, the 's are contained in the maximal invariant set of .
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Article dans une revue
Mathematische Zeitschrift, Springer, 2016, 282 (3-4), pp.889 - 912. 〈http://link.springer.com/article/10.1007%2Fs00209-015-1569-6〉. 〈10.1007/s00209-015-1569-6〉
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01413416
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 9 décembre 2016 - 17:16:58
Dernière modification le : lundi 4 décembre 2017 - 10:36:47

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F. Beguin, C. Bonatti, B. Yu. A spectral-like decomposition for transitive Anosov flows in dimension three. Mathematische Zeitschrift, Springer, 2016, 282 (3-4), pp.889 - 912. 〈http://link.springer.com/article/10.1007%2Fs00209-015-1569-6〉. 〈10.1007/s00209-015-1569-6〉. 〈hal-01413416〉

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