On invariant volumes of codimension-one Anosov flows and the Verjovsky conjecture |
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Authors: | Masayuki Asaoka |
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Affiliation: | (1) Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan |
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Abstract: | We show that any topologically transitive codimension-one Anosov flow on a closed manifold is topologically equivalent to a smooth Anosov flow that preserves a smooth volume. By a classical theorem due to Verjovsky, any higher-dimensional codimension-one Anosov flow is topologically transitive. Recently, Simić showed that any higher-dimensional codimension-one Anosov flow that preserves a smooth volume is topologically equivalent to the suspension of an Anosov diffeomorphism. Therefore, our result gives a complete classification of codimension-one Anosov flows up to topological equivalence in higher dimensions. |
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