Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A pathological flow in the torus

Author: Anatole Beck
Journal: Proc. Amer. Math. Soc. 82 (1981), 303-306
MSC: Primary 54H20; Secondary 28A75
MathSciNet review: 609672
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In a recent book (Continuous flows in the plane, Springer Grundlehren, vol. 201, 1974) the author of this article comments that there exist flows in the plane which have the property that some of their orbits have positive planar measure. Indeed, there are flows with the property that the complement of a countable set of orbits has measure 0. This fact does not appear in the literature, and the author has been asked to provide a proof. He proves instead the existence of a continuous flow in the torus in which the complement of a single orbit has measure 0. Then, lifting the torus to the plane gives the other example.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H20, 28A75

Retrieve articles in all journals with MSC: 54H20, 28A75

Additional Information

Keywords: Osgood curve, curve of positive area, irrational flow
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society