Analytical renormalization results for the cross-over behavior of period doubling, from conservative to dissipative systems

G. Reinout, G. Reinout W. Quispel

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has been shown that there is a universal scaling function describing the cross-over of the effective Feigenbaum convergence rate δ from its conservative value (δ = 8.721097 ....), as a function of the “effective dissipation”. Using renormalization theory I obtain an explicit analytical expression for this cross-over function and show that it's not monotonic but has a minimum, just before it reaches its asymptotic dissipative value. I also derive an analytical expression for the (period-doubling) bifurcation values in a particular map (the Hénon map), at all values of the Jacobian.
Original languageUndefined
Pages (from-to)477-478
JournalPhysica D
Issue number1-3
Publication statusPublished - 1986
Externally publishedYes


  • IR-69647

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