ABSTRACT
The dynamical system associated to the difference equation Δ 2 x n = k 2 π sin ( 2 π x n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003069515/f3ef54a9-ca7f-48a5-bad6-5d54427f48cf/content/eq2522.tif"/>
has been studied numerically by several authors. On the basis of numerical evidence, they conclude that there exists a number k 0 ≈ 0.97 such that there are homotopically non-trivial invariant circles for |k| ≤ k 0 and there are none for |k| > k 0. In this note, we give a simple rigorous proof that there are none for | k | > 4 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003069515/f3ef54a9-ca7f-48a5-bad6-5d54427f48cf/content/eq2523.tif"/> .
