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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{beguin2026from,
  title = {{From Markovian actions to Anosov flows}},
  author = {François Béguin and Ioannis Iakovoglou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.25604},
  eprint = {2607.25604},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.25604},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - From Markovian actions to Anosov flows
AU  - François Béguin
AU  - Ioannis Iakovoglou
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2607.25604
UR  - https://arxiv.org/abs/2607.25604
AB  - 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.
ER  -