SpringerLink
Log in

On the Invariant Tori of Quasilinear Countable Systems of Differential Equations Defined on Infinite–Dimensional Tori

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We consider a countable quasilinear system of differential equations defined on an infinite-dimensional torus. The problem is to find sufficient conditions under which the investigated system of equations possesses an invariant torus in the space of bounded numerical sequences whose generating function can be approximated with any given accuracy by a generating function of the invariant torus for some countable linear system defined on a finite-dimensional torus. This enables us to approximate (with any given degree of accuracy) a one-parameter family of solutions almost periodic in Bohr’s sense of a given system of equations by a family of quasiperiodic solutions of the above-mentioned linear system uniformly in the parameter.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. V. Nemytskii, Oscillations in Autonomous Systems. Fifth Summer Mathematical School [in Russian], Naukova Dumka, Kiev (1968).

  2. P. G. Bohl, Selected Works [in Russian], Akad. Nauk Latv. SSR, Riga (1961).

    Google Scholar 

  3. B. M. Levitan, Almost Periodic Functions [in Russian], Gostekhizdat, Moscow (1953).

    MATH  Google Scholar 

  4. B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).

    MATH  Google Scholar 

  5. A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  6. A. M. Samoilenko and Yu. V. Teplinskii, Countable Systems of Differential Equations, VSP, Utrecht (2003).

    Book  Google Scholar 

  7. Yu. A. Mitropol’skii, A. M. Samoilenko, and V. L. Kulik, Investigation of the Dichotomy of Linear Systems of Differential Equations with the Use of the Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).

  8. A. M. Samoilenko and Y. V. Teplinsky, Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces, World Scientific, Hackensack (2013).

    Book  Google Scholar 

  9. Yu. V. Teplins’kyi, Invariant Tori of Differential-Difference Equations in Spaces of Bounded Numerical Sequences [in Ukrainian], Kam’yanets-Podilskyi National University, Kam’yanets-Podilskyi (2015).

  10. K. P. Persidskii, Infinite Systems of Differential Equations. Differential Equations in Nonlinear Spaces [in Russian], Nauka, Alma-Ata (1976).

Download references

Author information

Authors and Affiliations

  1. I. Ohienko Kam’yanets-Podilsky National University, Ohienko Str., 61, Kam’yanets-Podilskyi, 32300, Ukraine

    Yu. V. Teplinsky

Authors
  1. Yu. V. Teplinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. V. Teplinsky.

Additional information

Translated from Neliniini Kolyvannya, Vol. 23, No. 4, pp. 553–564, October–December, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Teplinsky, Y.V. On the Invariant Tori of Quasilinear Countable Systems of Differential Equations Defined on Infinite–Dimensional Tori. J Math Sci 263, 327–340 (2022). https://doi.org/10.1007/s10958-022-05928-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-022-05928-3

Search

Navigation