ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Mukhin R. R. Dynamical chaos: the difficult path discovering. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 4, pp. 43-54. DOI: 10.18500/0869-6632-2014-22-4-43-54

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 134)
Article type: 

Dynamical chaos: the difficult path discovering

Mukhin Ravil Rafkatovich, Stary Oskol technological Institute. A. A. Ugarov (branch) of Federal state educational institution of higher professional education "national research technological University "MISIS" (STI nust Misa)

Dynamic chaos – a remarkable milestone development of science of the last centuryhas attracted the attention of different areas of knowledge. Chaos theory describes not only a wide range of phenomena in various fields of physics and other natural sciences and penetrates into the humanitarian sphere, but also significantly influenced the scientific picture of the world. What features of the development of science, economic and social conditions led to that long and difficult path of discovery of chaos began precisely at the end of the XIX century and stretched out for decades? Finding answers to these questions is the subject of this paper.

  1. Einstein А. Autobiographical Notes. Open Court; 1949.
  2. Gemmer M. The Evolution of the Concepts of Quantum Mechanics. Moscow: Nauka; 1985. 384 p. (in Russian).
  3. Van der Pol D, van der Mark J. Frequency demultiplication. Nature. 1927;120(3019):363—364. DOI: 10.1038/120363a0.
  4. Cartwrighte M, Littlewood JE. On non-linear differential equation of the second order. Annals of Mathematics. 1947;48(2):472—494. DOI: 10.2307/1969181.
  5. Molodshiy VP. O. Cauchy and the revolution in mathematical analysis of the first quarter of the XIX century. In: Historical and Mathematical Research (Collection of Articles). No. 23. Moscow: Nauka; 1978. P. 32—55 (in Russian).
  6. Kolmogoroff AN. General theory of dynamical systems and classical mechanics. Proc. Intern. Congr. Math. 1954;1:315—333.
  7. Poincaré A. About Curves Defined by Differential Equations. Moscow-Leningrad: OGIZ; 1947. 392 p. (in Russian).
  8. Poincaré H. Sur le probleme des trois corps et les equations de la dynamique. Acta Math. 1890;13(1—2):1 (in French).
  9. Poincaré А. New Methods of Celestial Mechanics. AIP-Press; 1992. 1096 p.
  10. Anosov DV. Poincare and Oscar II problems. In: Historical and Mathematical Research. No. 6(41). Moscow: RFBR; 2001. P. 57—72 (in Russian).
  11. Birkhof J. Dynamical Systems. Rhode Island: AMS; 1927. 305 p.
  12. Grasyuk AZ, Oraevsky AN. Transient processes in a molecular generator. Radio Engineering and Electronic Physics. 1964;9(3):524—532 (in Russian).
  13. Lorenz E. Detrministic nonperiodic flow. J. Atmos. Sci. 1963;20(2):130—141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
  14. Arnol'd VI, Meshalkin LD. A. N. Kolmogorov's seminar on selected problems of analysis (1958/1959). Uspekhi Mat. Nauk. 1960;15(1):247–250 (in Russian).
  15. Aubin D, Dahan Dalmedico A. Writing the history of dynamical systems and chaos. Historia Mathematica. 2002;29(3):273—339. DOI: 10.1006/hmat.2002.2351.
  16. Dahan Dalmedico A. La renaissance des systemes dynamiques aux Etats-Unis apres la deuxieme guerre mondiale. Suppl. Rendiconti dei circolo math. Palermo. 1994;34:133 (in French).
  17. Oraevsky AN. Oral report 17.04.2003.
  18. Henon M, Heiles C. The applicability of the third integral of motion: Some numerical experiments. Astron. J. 1964;69(1)73.
  19. Sretensky LN. The Work of Henri Poincaré. Questions of History, Natural Science and Technology. 1963;15:30 (in Russian).
  20. Dahan Dalmedico A. History and epistemology of models: Meteorology (1946–1963) as a case study. Archive for History of Exact Sciences. 2001;55(5):395—422. DOI: 10.1007/s004070000032.
  21. Shilnikov LP. Homoclinic trajectories: From Poincaré to the present day. In: Mathematical Events of the XX Century. Moscow: FAZIS; 2003. P. 466—489 (in Russian).
Short text (in English):
(downloads: 67)