Research Article

Flows with constant slope on the Klein bottle

Published in: Quaestiones Mathematicae
Volume 48 , issue 3 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 515–523
DOI: 10.2989/16073606.2024.2402926
Author(s): Luís Barreira Universidade de Lisboa, Portugal, Jaume Llibre Universitat Autònoma de Barcelona, Spain, Claudia Valls Instituto Superior Técnico, Universidade de Lisboa, Portugal,
Keywords: Primary: 34C05, Smooth flow with constant slope, Klein bottle, 2-dimensional torus,
Download full text Get new issue alerts

Abstract

We consider smooth flows with constant slope on the 2-dimensional (flat) torus and on the (flat) Klein bottle. It is well known that for a flow with constant slope on the torus either all orbits are periodic or all orbits are dense. We obtain a similar classification for the orbits of a flow with constant slope on the Klein bottle: again either all orbits are periodic, although some periods change, or all orbits are dense. This requires considering flows on the unit normal bundle of the Klein bottle.
« A note on fibers and Vietoris topologies of paratopological groups
Minimising the eccentricity index in trees with given segment sequence »

Get new issue alerts for Quaestiones Mathematicae

CAPTCHA Reload CAPTCHA