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Regular and Chaotic Dynamics, 2000, Volume 5, Issue 4, Pages 459–476
DOI: https://doi.org/10.1070/RD2000v005n04ABEH000159
(Mi rcd890)
 

This article is cited in 9 scientific papers (total in 9 papers)

On Scaling Properties of Two-Dimensional Maps Near the Accumulation Point of the Period-Tripling Cascade

O. B. Isaeva, S. P. Kuznetsov

Institute of Radio-Engineering and Electronics of RAS, Zelenaya 38, Saratov, 410019, Russia
Citations (9)
Abstract: We analyse dynamics generated by quadratic complex map at the accumulation point of the period-tripling cascade (see Golberg, Sinai, and Khanin, Usp. Mat. Nauk. V. 38, № 1, 1983, 159; Cvitanovic; and Myrheim, Phys. Lett. A94, № 8, 1983, 329). It is shown that in general this kind of the universal behavior does not survive the translation two-dimensional real maps violating the Cauchy–Riemann equations. In the extended parameter space of the two-dimensional maps the scaling properties are determined by two complex universal constants. One of them corresponds to perturbations retaining the map in the complex-analytic class and equals $\delta_1 \cong 4.6002 - 8.9812i$ in accordance with the mentioned works. The second constant $\delta_2 \cong 2.5872 + 1.8067i$ is responsible for violation of the analyticity. Graphical illustrations of scaling properties associated with both these constants are presented. We conclude that in the extended parameter space of the two-dimensional maps the period tripling universal behavior appears as a phenomenon of codimension $4$.
Received: 19.09.2000
Bibliographic databases:
Document Type: Article
MSC: 58F36
Language: English
Citation: O. B. Isaeva, S. P. Kuznetsov, “On Scaling Properties of Two-Dimensional Maps Near the Accumulation Point of the Period-Tripling Cascade”, Regul. Chaotic Dyn., 5:4 (2000), 459–476
Citation in format AMSBIB
\Bibitem{IsaKuz00}
\by O. B. Isaeva, S. P. Kuznetsov
\paper On Scaling Properties of Two-Dimensional Maps Near the Accumulation Point of the Period-Tripling Cascade
\jour Regul. Chaotic Dyn.
\yr 2000
\vol 5
\issue 4
\pages 459--476
\mathnet{http://mi.mathnet.ru/rcd890}
\crossref{https://doi.org/10.1070/RD2000v005n04ABEH000159}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1810626}
\zmath{https://zbmath.org/?q=an:0970.37035}
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