Abstract
Infinite sequences of period doubling bifurcations in one-parameter families (1-pf) of maps enjoy very strong universality properties: This is known numerically in a multitude of cases and has been shown rigorously for certain 1-pf of maps on the interval. These bifurcations occur in 1-pf of analytic maps at values of the parameter tending to a limit with the asymptotically geometric ratio 1 /4.6692 ....In this paper we indicate the main steps of a proof that the same is true for 1-pf of analytic maps from ℂn to ℂn, whose restriction to ℝn is real.
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Work supported by the Fonds National Suisse, and by the National Science Foundation under Grant PHY-79-16812.
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Collet, P., Eckmann, J.P. & Koch, H. Period doubling bifurcations for families of maps on ℝn . J Stat Phys 25, 1–14 (1981). https://doi.org/10.1007/BF01008475
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DOI: https://doi.org/10.1007/BF01008475