Scaling properties in dynamics of non-analytic complex maps near the accumulation point of the period-tripling cascade

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dc.creatorIsaeva, O. B.
dc.creatorKuznetsov, S. P.
dc.date2001-10-18
dc.date.accessioned2026-07-07T05:33:43Z
dc.date.available2026-07-07T05:33:43Z
dc.descriptionThe accumulation point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanovic and Myrheim (Phys.Lett. A94:8, 1983, 329). As we argue, in the extended parameter space of smooth maps, not necessary satisfying the Cauchy - Riemann equations, the scaling properties associated with the period-tripling are governed by two relevant universal complex constants. The first one is $δ_1 = 4.6002-8.9812i$ (in accordance with the mentioned works), while the other one, responsible for the violation of the analyticity, is found to be $δ_2 = 2.5872+1.8067i$. It means that in the extended parameter space the critical behaviour associated with the period-tripling cascade is a phenomenon of codimension four. Scaling properties of the parameter space are illustrated by diagrams in special local coordinates. We emphasize a necessity for a nonlinear parameter change to observe the parameter space scaling.
dc.description22 pages, 3 figures, 4 tables
dc.identifierhttps://arxiv.org/abs/nlin/0110032
dc.identifierhttp://arxiv.org/abs/nlin/0110032
dc.identifierO.B. Isaeva, S.P. Kuznetsov // Regular & Chaotic Dynamics. V.5, No.4 (2000) P.459
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80100
dc.subjectChaotic Dynamics
dc.titleScaling properties in dynamics of non-analytic complex maps near the accumulation point of the period-tripling cascade
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