A criterion for the non-existence of invariant circles
The purpose of this paper is to give a criterion for the existence of invariant circles for a certain class of area-preserving and monotone twist diffeomorphisms of the annulus. The author provides a numerical invariant, for each irrational number \(\omega\), which is always nonnegative, and which vanishes if and only if there is an invariant circle of frequency \(\omega\). The main idea of this paper comes from the version of Birkhoff's arguments for the billiard ball problem. However, the author has to introduce new concepts and to prove a series of propositions for the principal result of this paper, which will be omitted here because of their long statements. The interested reader is referred to this well- written paper.
scientific article; zbMATH DE number 3973899
scientific article