Abstract
A statement in a recent paper by Saito [61 suggested the following question: Does there exist on the torus an analytic, area preserving, ergodic flow which has a stationary point? The purpose of this note is to describe an elementary example of such a flow, and to discuss some properties of a topological class of flows to which it belongs. Stepanoff [7) (cf. also [4, pp. 395-400, 506-507]) considered the flows defined by equations of the form (1) where Y= aX, a is an irrational number, and X is periodic, non-negative, continuous, satisfies a Lipschitz condition in x and y, and vanishes at one and only one point of the torus. He showed that these flows are metrically transitive with respect to the invariant Borel measure
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
