Non-existence of invariant circles

Abstract

Abstract The dynamical system associated to the difference equation 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 |> .