Non-existence of invariant circles
- 1 June 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 4 (2) , 301-309
- https://doi.org/10.1017/s0143385700002455
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 numberk0≈ 0.97 such that there are homotopically non-trivial invariant circles for |k|≤k0and there are none for |k|>k0. In this note, we give a simple rigorous proof that there are none for |k|>.Keywords
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