Anomalous Anosov flows revisited

Thomas Barthelmé, Christian Bonatti, Andrey Gogolev, Federico Rodriguez Hertz

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows — they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In particular, this proves that the examples in dimension strictly greater than 3 described by Franks and Williams in Anomalous Anosov Flows cannot be Anosov flows. In the second part, we give a new surgery type construction of Anosov flows, based on Franks and Williams 3-dimensional example, which yields non-transitive Anosov flows in all odd dimensions.

Original languageEnglish (US)
JournalProceedings of the London Mathematical Society
DOIs
StateAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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