Cherry flows with non-trivial attractors
Volume 244 / 2019
Fundamenta Mathematicae 244 (2019), 243-253
MSC: 37E10, 37E35.
DOI: 10.4064/fm531-3-2018
Published online: 12 October 2018
Abstract
We provide an example of a Cherry flow (i.e. a ${{\mathcal C}^\infty }$ flow on the $2$-dimensional torus with a sink and a saddle) having a quasi-minimal set which is an attractor. The first return map for such a flow, also constructed in the paper, is a ${{\mathcal C}^\infty }$ circle map having a flat interval and a non-trivial wandering interval.
