title: Dynamical ordering of symmetric non-Birkhoff periodic points in reversible monotone twist mappings.
abstract: We study the coexistence of symmetric non-Birkhoff periodic orbits of C(1) reversible monotone twist mappings on the cylinder. We prove the equivalence of the existence of non-Birkhoff periodic orbits and that of transverse homoclinic intersections of stable and unstable manifolds of the fixed point. We derive the positional relation of symmetric Birkhoff and non-Birkhoff periodic orbits and obtain the dynamical ordering of symmetric non-Birkhoff periodic orbits. An extension of the Sharkovskii ordering to two-dimensional mappings has been carried out. In the proof of various properties of the mappings, reversibility plays an essential role. (c) 2002 American Institute of Physics.
authors.affiliation: National Astronomical Observatory, Mitaka, Tokyo 181-8588, Japan.
authors.forename: Kiyotaka
authors.initials: K
authors.lastname: Tanikawa
authors.forename: Yoshihiro
authors.initials: Y
authors.lastname: Yamaguchi