Prog. Theor. Phys. Vol. 118 No. 4 (2007) pp. 675-699
Non-Birkhoff Periodic Orbits of Farey Type and Dynamical Ordering in the Standard Mapping. II
1Teikyo Heisei University, Ichihara 290-0193, Japan
2National Astronomical Observatory, Mitaka 181-8588, Japan
(Received July 26, 2007)
Using dynamical ordering for symmetric non-Birkhoff periodic
orbits of Farey type (NBF), the properties of the limit at which the
rotation numbers of NBFs accumulate to a rational number or irrational number are studied in the case of the standard mapping. Next, the relation between
the critical value at which the KAM curve disappears and the critical
value at which NBF appears is derived. The slow orbit connecting
the two resonance chains is found.
DOI : 10.1143/PTP.118.675
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Citing Article(s) :
Progress of Theoretical Physics Vol. 119 No. 4 (2008) pp. 533-559
On Mather's Connecting Orbits in Standard Mapping
Yoshihiro Yamaguchi and Kiyotaka Tanikawa