Scaling of the “superstable” fraction of the 2D period-doubling interval

G.R.W. Quispel

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The scaling properties of a “superstable” parameter interval,ℓ , where the eigenvalues about a period-2n orbit are complex, are derived for 2D period-doubling maps. The ratio ofℓ to the whole parameter interval, between the nth and the (n+1)st bifurcation, is shown to be a universal function of the effective jacobian, Be, only (Be≡B2n, B is the jacobian of th e map). Unlike the whole period-2n interval,ℓ has a convergence rate that behaves as 4.6692016xB 1/4 as Be↓), while its complement has a convergence rate 8.7210972/4 as Be↑1.
Original languageUndefined
Pages (from-to)353-356
JournalPhysics letters A
Issue number8
Publication statusPublished - 1985
Externally publishedYes


  • IR-69520

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