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Symbolic dynamics and systematics of periodic windows

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  • Hao, Bai-lin

Abstract

Elementary symbolic dynamics of two or more letters, developed for one-dimensional mappings, may be of much help in studying ODE's. At least three periodically driven systems, including one studied in great detail by us, are known to be described in the large by symbolic dynamics of two letters. The skeleton of periodic windows in the Lorenz model is described by symbolic dynamics of three letters in close connection with the one-dimensional antisymmetric cubic map. The understanding of transitions from quasiperiodicity to chaos may also be deepened, looking at the global picture of the interrelation between the U-sequences and the Farey sequences.

Suggested Citation

  • Hao, Bai-lin, 1986. "Symbolic dynamics and systematics of periodic windows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 85-95.
    • Handle: RePEc:eee:phsmap:v:140:y:1986:i:1:p:85-95
    DOI: 10.1016/0378-4371(86)90208-6
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