title: Shape of analyticity domains of Lindstedt series: the standard map.
abstract: The analyticity domains of the Lindstedt series for the standard map are studied numerically using Padé approximants to model their natural boundaries. We show that if the rotation number is a Diophantine number close to a rational value p/q, then the radius of convergence of the Lindstedt series becomes smaller than the critical threshold for the corresponding Kol'mogorov-Arnol'd-Moser curve, and the natural boundary on the plane of the complexified perturbative parameter acquires a flower-like shape with 2q petals.
authors.affiliation: Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Berretti
authors.forename: C
authors.initials: C
authors.lastname: Falcolini
authors.forename: G
authors.initials: G
authors.lastname: Gentile