THE ROLE OF CODIMENSION IN DYNAMICAL SYSTEMS

Jason A.C. Gallas
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Jason A.C. Gallas: Laboratory for Plasma Research, University of Maryland, College Park, MD 20742, USA;

International Journal of Modern Physics C (IJMPC), 1992, vol. 03, issue 06, 1295-1321

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.

Keywords: Isoperiodic Diagrams; Codimension-two Systems; Hénon Map (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1142/S0129183192000890

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