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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 δ14.60028.9812iδ14.60028.9812i in accordance with the mentioned works. The second constant δ22.5872+1.8067iδ22.5872+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 44.
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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  • https://www.mathnet.ru/eng/rcd890
  • https://www.mathnet.ru/eng/rcd/v5/i4/p459
  • This publication is cited in the following 9 articles:
    1. O. B. Isaeva, M. A. Obychev, D. V. Savin, “Dinamika diskretnoi sistemy s operatorom evolyutsii, zadavaemym neyavnoi funktsiei: ot otobrazheniya Mandelbrota k unitarnomu otobrazheniyu”, Nelineinaya dinam., 13:3 (2017), 331–348  mathnet  crossref  elib
    2. Andreas Prokoph, Stephen J. Puetz, “Period-Tripling and Fractal Features in Multi-Billion Year Geological Records”, Math Geosci, 47:5 (2015), 501  crossref
    3. Olga B. Isaeva, Sergey P. Kuznetsov, Andrew H. Osbaldestin, “A system of alternately excited coupled non-autonomous oscillators manifesting phenomena intrinsic to complex analytical maps”, Physica D: Nonlinear Phenomena, 237:7 (2008), 873  crossref
    4. O. B. Isaeva, “Fourier spectrum of the signal generated at the point of period tripling bifurcation accumulation”, Tech. Phys., 51:7 (2006), 929  crossref
    5. Alexander P. Kuznetsov, Sergey P. Kuznetsov, Julia V. Sedova, “Effect of noise on the critical golden-mean quasiperiodic dynamics in the circle map”, Physica A: Statistical Mechanics and its Applications, 359 (2006), 48  crossref
    6. S. P. Kuznetsov, A. P. Kuznetsov, I. R. Sataev, “Multiparameter Critical Situations, Universality and Scaling in Two-Dimensional Period-Doubling Maps”, J Stat Phys, 121:5-6 (2005), 697  crossref
    7. Sergey V. Shepel, Brian L. Smith, Samuel Paolucci, “Implementation of a Level Set Interface Tracking Method in the FIDAP and CFX-4 Codes”, Journal of Fluids Engineering, 127:4 (2005), 674  crossref
    8. Sergey P. Kuznetsov, “Effect of noise on the dynamics at the torus-doubling terminal point in a quadratic map under quasiperiodic driving”, Phys. Rev. E, 72:2 (2005)  crossref
    9. Olga B. Isaeva, Sergey P. Kuznetsov, Andrew H. Osbaldestin, “Effect of noise on the dynamics of a complex map at the period-tripling accumulation point”, Phys. Rev. E, 69:3 (2004)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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