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


Quispel, G.R.W. (1985) Scaling of the “superstable” fraction of the 2D period-doubling interval. Physics Letters A, 112 (8). pp. 353-356. ISSN 0375-9601

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Abstract: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.

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Copyright:© 1985 Elsevier Science
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