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Published on: May 19, 2014
Dynamical ordering of symmetric non-Birkhoff periodic points in reversible monotone twist mappings
Kiyotaka Tanikawa1, Yoshihiro Yamaguchi
1National Astronomical Observatory, Mitaka, Tokyo 181-8588, Japan.
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.
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