Nonabsolutely Continuous Foliations for an Anosov Diffeomorphism.

Lai-Sang Young; Clark Robinson

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This paper concerns projectively Anosov flows $φ^{t}$ with smooth stable and unstable foliations $ℱ^{s}$ and $ℱ^{u}$ on a Seifert manifold $M$ . We show that if the foliation $ℱ^{s}$ or $ℱ^{u}$ contains a compact leaf, then the flow $φ^{t}$ is decomposed into a finite union of models which are defined on $T^{2} \times I$ and bounded by compact leaves, and therefore the manifold $M$ is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which...

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We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on $T^{2}$ which can be extended on a neighbourhood of $T^{2}$ into a projectively Anosov flow so that $T^{2}$ is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on $T^{3}$ . In this case, the only flows on $T^{2}$ which...

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We consider transversely affine foliations without compact leaves of higher genus surface bundles over the circle of pseudo-Anosov type such that the Euler classes of the tangent bundles of the foliations coincide with that of the bundle foliation. We classify such foliations of those surface bundles whose monodromies satisfy a certain condition.