Action on the circle at infinity of foliations of

  • Christian Bonatti

    Université de Bourgogne, Dijon, France
Action on the circle at infinity of foliations of ${\mathbb{R}}^{2}$ cover

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Abstract

This paper provides a canonical compactification of the plane by adding a circle at infinity associated to a countable family of singular foliations or laminations (under some hypotheses), generalizing an idea by Mather (1982). Moreover, any homeomorphism of preserving the foliations extends on the circle at infinity. Then, this paper provides conditions ensuring the minimality of the action on the circle at infinity induced by an action on preserving one foliation or two transverse foliations. In particular, the action on the circle at infinity associated to an Anosov flow on a closed -manifold is minimal if and only if is non--covered.

Cite this article

Christian Bonatti, Action on the circle at infinity of foliations of . Enseign. Math. (2024), published online first

DOI 10.4171/LEM/1086