title: Integrable approximation of regular regions with a nonlinear resonance chain.
abstract: Generic Hamiltonian systems have a mixed phase space where regions of regular and chaotic motion coexist. We present a method for constructing an integrable approximation to such regular phase-space regions including a nonlinear resonance chain. This approach generalizes the recently introduced iterative canonical transformation method. In the first step of the method a normal-form Hamiltonian with a resonance chain is adapted such that actions and frequencies match with those of the nonintegrable system. In the second step a sequence of canonical transformations is applied to the integrable approximation to match the shape of regular tori. We demonstrate the method for the generic standard map at various parameters.
authors.affiliation: Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany and Institut für Theoretische Physik, Universität Magdeburg, Postfach 4120, 39016 Magdeburg, Germany.
authors.forename: Julius
authors.initials: J
authors.lastname: Kullig
authors.affiliation: Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
authors.forename: Clemens
authors.initials: C
authors.lastname: Löbner
authors.affiliation: Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany and Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji 192-0397, Japan.
authors.forename: Normann
authors.initials: N
authors.lastname: Mertig
authors.affiliation: Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
authors.forename: Arnd
authors.initials: A
authors.lastname: Bäcker
authors.affiliation: Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
authors.forename: Roland
authors.initials: R
authors.lastname: Ketzmerick