Skip to main content
SpringerLink
Log in

Linear extensions of dynamic systems and the reductibility problem

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

The relation of linear extensions of smooth dynamic systems to cohomologies and to reducibility in the case of flow is investigated. A result is obtained concerning Γ-cohomologies in the neighborhood of a constant cocycle for the case of an arbitrary closed subgroup Γ of the group GL (k, C).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. A. A. Kirillov, “Dynamic systems, factors, and group representations,” Uspekhi Matem. Nauk,22, No. 5, 65–79 (1967).

    Google Scholar 

  2. B. F. Bylov, R. É. Vinograd, D. M. Grobman, and V. V. Nemytskii, The Theory of Lyapunov Exponents [in Russian], Moscow (1966).

  3. A. E. Gel'man, “Reducibility of a class of systems with quasiperiodic coefficients,” Dokl. Akad. Nauk SSSR,116, No. 4, 535–537 (1957).

    Google Scholar 

  4. A. E. Gel'man, “Reducibility of systems with quasiperiodic matrices,” Dif. Uravneniya,1, No. 3, 283–294 (1965).

    Google Scholar 

  5. L. Ya. Adrianova, “Reducibility of a system of n linear differential equations with quasiperiodic coefficients,” Vestnik Leningr. Un-ta, Ser. Matern., Mekh. i Astr., No. 7, 2, 14–24 (1962).

    Google Scholar 

  6. I. N. Blinov, “The analytic representation of solutions of a system of linear differential equations with almost-periodic coefficients depending on a parameter,” Dif. Uravneniya,1, No. 8, 1042–1053 (1965).

    Google Scholar 

  7. O. B. Lykova, “Quasiperiodic solutions of a system differing slightly from a canonical system,” Ukrainsk. Matem. Zh.,16, No. 6, 752–768 (1964).

    Google Scholar 

  8. Yu. A. Mitropol'skii and A. M. Samoilenko, “Construction of solutions of linear differential equations with quasiperiodic coefficients by the accelerated convergence method,” Ukrainsk. Matem. Zh.,17, No. 6, 42–59 (1965).

    Google Scholar 

  9. V. I. Arnol'd, “Small denominators and problems of the stability of motion in classical and celestial mechanics,” Uspekhi Matem. Nauk,18, No. 6, 91–192 (1963).

    Google Scholar 

  10. Yu. Mozer, “The expansion of conditionally periodic motion in a convergent power series,” Uspekhi Matem. Nauk,24, No. 2, 165–211 (1969).

    Google Scholar 

  11. Yu. Mozer, “A rapidly convergent iterative method of solving differential equations,” Uspekhi Matem. Nauk,23, No. 4, 179–238 (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    S. B. Katok

Authors
  1. S. B. Katok
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 451–462, October, 1970.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Katok, S.B. Linear extensions of dynamic systems and the reductibility problem. Mathematical Notes of the Academy of Sciences of the USSR 8, 722–728 (1970). https://doi.org/10.1007/BF01104372

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01104372

Keywords

Search

Navigation