Skip to main content
SpringerLink
Log in

Recurrence of the integral of an odd conditionally periodic function

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We prove that the integral of a sufficiently smooth odd conditionally periodic function with zero mean and incommensurable frequencies recurs. Furthermore, we obtain the lower and upper bounds for smoothness guaranteeing the recurrence of the integral.

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

References

  1. H. Poincaré,On curves defined by differential equations [Russian translation], Gostekhizdat, Moscow-Leningrad (1947).

    Google Scholar 

  2. E. A. Sidorov, “On conditions for uniform stability (in the sense of Poisson) of cylindrical systems,”Uspekhi Mat. Nauk [Russian Math. Surveys],34, No. 6, 184–188 (1979).

    MATH  MathSciNet  Google Scholar 

  3. V. V. Kozlov,Methods of Qualitative Analysis in Dynamics of Solids [in Russian], Izd. Moskov. Univ., Moscow (1980).

    Google Scholar 

  4. N. G. Moshchevitin, “Recurrence of the integral of a smooth three-frequency conditionally periodic function,”Mat. Zametki [Math. Notes],58, No. 5, 723–735 (1985).

    MathSciNet  Google Scholar 

  5. N. G. Moshchevitin, “Nonrecurrence of the integral of a conditionally periodic function,”Mat. Zametki [Math. Notes],49, No. 6, 138–140 (1991).

    MATH  MathSciNet  Google Scholar 

  6. V. G. Sprindzhuk, “Asymptotic behavior of the integrals of quasiperiodic functions,”Differentsial'nye Uravneniya [Differential Equations],3, No. 6, 862–868 (1967).

    MATH  Google Scholar 

  7. V. G. Sprindzhuk, “Quasiperiodic functions with unbounded indefinite integral,” Dokl. Akad. Nauk BSSR,12, No. 1, 5–8 (1968).

    MATH  MathSciNet  Google Scholar 

  8. L. G. Peck, “On uniform distribution of algebraic numbers,”Proc. Amer. Math. Soc.,4, No. 1, 440–443 (1953).

    MATH  MathSciNet  Google Scholar 

  9. N. G. Moshchevitin, “The final properties of integrals of conditionally periodic functions related to the problem of small denominators,”Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] No. 5, 94–96 (1988).

    MATH  MathSciNet  Google Scholar 

  10. N. G. Moshchevitin, “The uniform distribution of the fractional parts of the systems of linear functions,”Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] No. 4, 26–31 (1990).

    MATH  MathSciNet  Google Scholar 

  11. N. G. Moshchevitin, “The behavior of the integral of a conditionally periodic function,”Mat. Zametki [Math. Notes],50, No. 3, 97–106 (1991).

    MATH  MathSciNet  Google Scholar 

  12. N. G. Moshchevitin, “Distribution of values of linear functions and asymptotic behavior of trajectories of some dynamical systems,”Mat. Zametki [Math. Notes],58, No. 3, 394–410 (1995).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    S. V. Konyagin

Authors
  1. S. V. Konyagin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 570–577, April, 1997.

Translated by N. K. Kulman

Rights and permissions

Reprints and permissions

About this article

Cite this article

Konyagin, S.V. Recurrence of the integral of an odd conditionally periodic function. Math Notes 61, 473–479 (1997). https://doi.org/10.1007/BF02354991

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02354991

Key words

Search

Navigation