Quantitative perturbation theory by successive elimination of harmonics (Q1209262)

This paper establishes the theoretical basis for the method presented by the first author [see the previous review, ibid., 101-130 (1993)]. Two theorems are proved. The first one proves the ``almost invariantness within the limit \(T\) in time'' of tori constructed by the method. These tori fill up in the phase space an open set \(A\), say. The second theorem presents an estimate for \(T\) of exponential type that guarantees that the set \(A\) contains open balls of a given radius.