Geodesic
50th anniversary of the discovery of Feigenbaum's patterns
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 33 (2025) no. 1, pp. 5-8.

Voir la notice de l'article provenant de la source Math-Net.Ru

In 1975, while experimenting with a pocket programmable calculator, American physicist Mitchell Feigenbaum discovered the universal patterns of transition to chaos through period doubling bifurcations, which now bear his name.
Keywords: Feigenbaum's patterns 
@article{IVP_2025_33_1_a0,
     author = {A. P. Kuznetsov and Yu. V. Sedova},
     title = {50th anniversary of the discovery of {Feigenbaum's} patterns},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {5--8},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2025_33_1_a0/}
}
TY  - JOUR
AU  - A. P. Kuznetsov
AU  - Yu. V. Sedova
TI  - 50th anniversary of the discovery of Feigenbaum's patterns
JO  - Izvestiya VUZ. Applied Nonlinear Dynamics
PY  - 2025
SP  - 5
EP  - 8
VL  - 33
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVP_2025_33_1_a0/
LA  - ru
ID  - IVP_2025_33_1_a0
ER  - 
%0 Journal Article
%A A. P. Kuznetsov
%A Yu. V. Sedova
%T 50th anniversary of the discovery of Feigenbaum's patterns
%J Izvestiya VUZ. Applied Nonlinear Dynamics
%D 2025
%P 5-8
%V 33
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVP_2025_33_1_a0/
%G ru
%F IVP_2025_33_1_a0
A. P. Kuznetsov; Yu. V. Sedova. 50th anniversary of the discovery of Feigenbaum's patterns. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 33 (2025) no. 1, pp. 5-8. http://geodesic.mathdoc.fr/item/IVP_2025_33_1_a0/

[1] Myrberg P. J., “Iteration der reellen Polynome zweiten Grades III”, Ann. Acad. Sci. Fenn. Ser. A, 1963, no. 336/3, 1–18 | DOI | MR

[2] Sharkovskii A. M., “Sosuschestvovanie tsiklov nepreryvnogo preobrazovaniya pryamoi v pryamuyu”, Ukr. mat. zhurn, 26:1 (1964), 61

[3] Metropolis N., Stein R. K., Stein M. L., “Finite limit sets for transformations of the unit interval”, J. Comb. Theory, 15:1 (1973), 25–44 | DOI | Zbl

[4] Feigenbaum M. J., “Quantitative universality for a class of nonlinear transformations”, J. Stat. Phys., 19:1 (1978), 25–52 | DOI | Zbl

[5] Feigenbaum M. J., “The universal metric properties of nonlinear transformations”, J. Stat. Phys., s21:6 (1979), 669–706 | DOI | Zbl

[6] Feigenbaum M., “Universalnost v povedenii nelineinykh sistem”, Uspekhi fizicheskikh nauk, 141:10 (1983), 343–374 | DOI

[7] Kuznetsov A. P., Kuznetsov S. P., “Kriticheskaya dinamika odnomernykh otobrazhenii. Chast 1. Stsenarii Feigenbauma”, Izvestiya vuzov. PND, 1:1 (1993), 15–33

[8] Kuznetsov S. P., Dinamicheskii khaos: Ucheb. posobie dlya vuzov, 2, pererab. i dop., Fizmatlit, M., 2006, 356 pp.

[9] Chang S. J., Wortis M., Wright J. A., “Iterative properties of a one-dimensional quartic map. Critical lines and tricritical behavior”, Phys. Rev. A, 25:5 (1981), 2669–2684 | DOI

[10] Kuznetsov A. P., Kuznetsov S. P., Sataev I. R., “Kriticheskaya dinamika odnomernykh otobrazhenii. Chast II. Dvukhparametricheskii perekhod k khaosu”, Izvestiya vuzov. PND, 1:3 (1993), 17–35

[11] Hirsch J. E., Nauenberg M., Scalapino D. J., “Intermittency in the presence of noise: A renormalization group formulation”, Physics Letters A, 87:8 (1982), 391–393 | DOI

[12] Hu B., Rudnick J., “Exact solutions to the Feigenbaum renormalization-group equations for intermittency”, Phys. Rev. Lett., 48:24 (1982), 1645–1648 | DOI

[13] Feigenbaum M. J., Kadanoff L. P., Shenker S. J., “Quasiperiodicity in dissipative systems: a renormalization group analysis”, Physica D, 5:2–3 (1982), 370–386 | DOI

[14] Ostlund S., Rand D., Sethna J., Siggia E., “Universal properties of the transition from quasi-periodicity to chaos in dissipative systems”, Physica D, 8:3 (1983), 303–342 | DOI

[15] Kuznetsov S. P., “Universalnost i podobie v povedenii svyazannykh sistem Feigenbauma”, Izvestiya vuzov. Radiofizika, 28:8 (1985), 991–1007

[16] Kook H., Ling F. H., Schmidt G., “Universal behavior of coupled nonlinear systems”, Phys. Rev. A, 43:6 (1991), 2700 | DOI

[17] Kim S. Y., Kook H., “Critical behavior in coupled nonlinear systems”, Phys. Rev., 46:8 (1992), R4467-R4470 | DOI

[18] Kim S. Y., Kook H., “Period doubling in coupled maps”, Phys. Rev. E, 48:2 (1993), 785 | DOI