From Markovian actions to Anosov flows

François Béguin; Ioannis Iakovoglou

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arXiv · 2607.25604

From Markovian actions to Anosov flows

François Béguin·Ioannis Iakovoglou

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Abstract

In this paper, we establish a necessary and sufficient condition for a group action on a bifoliated plane to arise from a topological Anosov flow supported by an orientable $3$-manifold. More precisely, we show that a group action on a non-singular bifoliated plane arises from such a flow if and only if it is an orientation preserving strong Markovian action, that is, an orientation preserving action of the plane preserving a family of rectangles satisfying suitable Markov-type properties. Furthermore, we prove that this family of rectangles can be lifted to a Markov partition of the associated flow.

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François Béguin, Ioannis Iakovoglou. 2026-07-28. From Markovian actions to Anosov flows. https://arxiv.org/abs/2607.25604

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