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Author(s):
Y.Nomura, Yoshi.H.Ichikawa and W.Horton
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Title:
Stabilities of Regular Motion in the Relativistic Standard Map
Date of publication:
Feb. 1991
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Key words:
relativistic standard map, chaotic motion, regular motion, involution decomposition, symmetry lines, periodic orbits, stability, residue, Poincare-Birkhoff muItifurcation, period-doubling bifurcation, period-3 catastrophe
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Abstract:
Analysis of the relativistic standard map is one of the important problems to understand nonlinear interaction between waves and charged particles in the relativistic dynamics. In the relativistic standard map, in general, chaotic motion is strongly suppressed and regular motion such as periodic orbit plays dominant roles in the phase space. Location of periodic points is predicted by use of symmetry lines of the map. Local stability of periodic points is investigated by introducing the residue of the orbit which characterizes the eigenvalue of the area-preserving map. It is found that the exchange of stable and unstable points takes place at some value of the relativistic parameter. Special behavior of the residue of the Poincare-Birkhoff period-4 points are also examined and related bifurcations are clarified.
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