D. Tischler, R. W. Tischler

1974

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Journal

Annales de l'Institut Fourier

Abstract

This paper considers locally free differentiable actions of R/ 1 "" 1 on a compact orientable n-manifold which have no compact orbits. For such an action, it is known that all orbits are isomorphic to where ^ lc is the /c-torus [I], We associate to such an action collection of rotation numbers which are elements of an action is free it is topologically conjugate (i.e. in a parameter preserving sense) to a linear action on a torus, one of the rotation numbers is sufficiently irrational (i.e. a Liouville inequality). Theorem 2 treats the case of a sufficiently irrational rotation and k ^ 0.

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