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Author(s):
Y. Nomura, S. Y. Kim, T. Kamimura and Y. H. Ichikawa
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Title:
Symmetry and Island Structure of the Standard Map
Date of publication:
Feb. 1990
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Key words:
2D area preserving mapping, reversible dynamical system, involution decomposition, periodic orbits, symmetry curves, standard map, Poincare-Birkhoff period-q islands
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Abstract:
Eveen though our primary interest is concerned with stochastic properties of the low dimensional nonlinear dynamical systems identification of the fixed points and analysis of the periodic orbits are necessary and unavoidable step in the studies of chaotic behaviour. For the case of 2-D area preserving mapping, the symmetry properties of the map provides critical information on the island structure of the mappings. In ouder to illustrate usefulness of knowledge of the symmetry properties, the periodic orbits of the standard map are discussed in detail by contructing the families of symmetry curves.
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