Numerical computation of rotation numbers of quasi-periodic planar curves (Q1038452)

The authors present numerical algorithms to deal with quasi-periodic invariant curves of planar maps by adapting a method given by \textit{T. M. Seara} and \textit{J. Villanueva} [Physica D 217, No.~2, 107--120 (2006; Zbl 1134.37339)] to compute rotation numbers of an analytic circle diffeomorphisms. The approach consists in computing a suitable average of the iterates of the map to obtain a new curve for which the direct projection onto a circle is well posed. This method can be applied to more general contexts because the construction does not use the invariance of the quasi-periodic curve under the map. Several examples are given to illustrate the method.