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Cherry flows with non-trivial attractors

Volume 244 / 2019

Liviana Palmisano 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.

Authors

  • Liviana PalmisanoUppsala University
    Uppsala, Sweden
    e-mail

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