Converse KAM: theory and practice
Whereas KAM theory deals with the existence of invariant circles of area preserving maps, the present paper is concerned with ``converse KAM theorems'', i.e. criteria for nonexistence of invariant circles. There are several such theorems available in the literature, which are ''unified, extended, reinterpreted, and applied''. As an example a computer proof is given for the fact that the so-called ``standard map'' \(p'=p-(k/2\pi) \sin 2\pi x\), \(x'=x+p'\) has no rotational invariant circles for \(| k| \geq 63/64\). The paper is self-contained and provides a useful survey of converse KAM theory.
invariant circles of area preserving maps
scientific article; zbMATH DE number 3938098