Symbolic encoding in symplectic maps

F Christiansen, A Politi

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

A general procedure to construct a generating partition in 2D symplectic maps is introduced. The implementation of the method, specifically discussed with reference to the standard map, can be easily extended to any model where chaos originates from a horseshoe-type mechanism. Symmetries arising from the symplectic structure of the dynamics are exploited to eliminate the remaining ambiguities of the encoding procedure, so that the resulting symbolic dynamics possesses the same symmetry as that of the original model. Moreover, the dividing line of the partition turns out to pass through the stability islands, in such a way as to yield a proper representation of the quasiperiodic dynamics as well as of the chaotic component. As a final confirmation of the correctness of our approach, we construct the associated pruning front and show that it is monotonous.

Original languageEnglish
Pages (from-to)1623-1640
Number of pages18
JournalNonlinearity
Volume9
Issue number6
Publication statusPublished - Nov 1996

Keywords

  • GENERATING PARTITIONS
  • HENON MAP

Cite this

Christiansen, F., & Politi, A. (1996). Symbolic encoding in symplectic maps. Nonlinearity, 9(6), 1623-1640.

Symbolic encoding in symplectic maps. / Christiansen, F ; Politi, A .

In: Nonlinearity, Vol. 9, No. 6, 11.1996, p. 1623-1640.

Research output: Contribution to journalArticle

Christiansen, F & Politi, A 1996, 'Symbolic encoding in symplectic maps', Nonlinearity, vol. 9, no. 6, pp. 1623-1640.
Christiansen F, Politi A. Symbolic encoding in symplectic maps. Nonlinearity. 1996 Nov;9(6):1623-1640.
Christiansen, F ; Politi, A . / Symbolic encoding in symplectic maps. In: Nonlinearity. 1996 ; Vol. 9, No. 6. pp. 1623-1640.
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