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The Role Of Codimension In Dynamical Systems

Author

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  • JASON A.C. GALLAS

    (Laboratory for Plasma Research, University of Maryland, College Park, MD 20742, USA;
    Laboratório de Óptica Quântica da UFSC, 88040–900 Florianópolis, Santa Catarina, Brazil)

Abstract

Isoperiodic diagrams are used to investigate the topology of the codimension space of a representative dynamical system: the Hénon map. The codimension space is reported to be organized in a simple and regular way: instead of “structures-within-structures” it consists of a “structures-parallel-to-structures” sequence of shrimp-shaped isoperiodic islands immersed on avia caotica. The isoperiodic islands consist of a main body of principal periodicityk=1, 2, 3, 4, …, which bifurcates according to a period-doubling route. ThePk=k×2n,n=0, 1, 2, …shrimps are very densely concentrated along a main α-direction, a neighborhood parallel to the lineb=−0.583a+1.025, where a andbare the dynamical parameters in Eq. (1). Isoperiodic diagrams allow to interpret and unify some apparently uncorrelated phenomena, such as ‘period-bubbling’, classes of reverse bifurcations and antimonotonicity and to recognize that they are in fact signatures of the complicated way in which period-doubling occurs in higher codimensional systems.

Suggested Citation

  • Jason A.C. Gallas, 1992. "The Role Of Codimension In Dynamical Systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 3(06), pages 1295-1321.
    • Handle: RePEc:wsi:ijmpcx:v:03:y:1992:i:06:n:s0129183192000890
    DOI: 10.1142/S0129183192000890
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