Skip to main content
SpringerLink
Log in

n-1 independent first integrals for linear differential systems in Rn and Cn

  • Published:
Qualitative Theory of Dynamical Systems Aims and scope Submit manuscript

Abstract

We prove that every linear system with constant coefficients on Rn or Cn is Darboux integrable by providing a complete explicit list ofn−1 independent Darboux first integrals.

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. R. M. Bulatovich,On the continuability of a gyroscopic integral from a linear system to a nonlinear system, Teor. Primen. Meh.21 (1995), 1–7.

    MathSciNet  Google Scholar 

  2. J. Chavarriga, J. Llibre andJ. Sotomayor,Algebraic solutions for polynomial systems with emphasis in the quadratic case, Exp. Math.15 (1997), 161–173.

    MATH  MathSciNet  Google Scholar 

  3. C. Christopher andJ. Llibre,Integrability via invariant algebraic curves for planar polynomial differential systems, Ann. of Differential Equations16 (2000), 5–19.

    MATH  MathSciNet  Google Scholar 

  4. C. Christopher, J. Llibre and J. V. Pereira,Multiplicity of invariant algebraic curves and Darboux integrability, Preprint 2000.

  5. G. Darboux,Memoire sur les équations differentielles algébrique du premier ordre et du premier degré (Mélanges), Bull. Sci. Math. 2ème série2 (1878), 60–96, 123–144, 151–200.

    Google Scholar 

  6. H. Flaschka, A.C. Newell andM. Tabor,Integrability, In What is Integrability? Ed. V.E. Zakharov, Springer-Verlag, Series in Nonlinear Dynamics, (1991), 71–114.

    Google Scholar 

  7. J. P. Jouanolou,Equations de Pfaff Algébriques, Lect. Notes in Math.708, Springer-Verlag, Berlin, (1979).

    MATH  Google Scholar 

  8. S. Maeda,On inheritance of quadratic first integral of linear system via Runge-Kutta methods, J. Math. Tokushima Univ.31 (1997), 63–67.

    MATH  MathSciNet  Google Scholar 

  9. J. Moulin Ollagnier andJ.M. Strelcyn,On first integrals of Linear systems, Frobenius integrability theorem and linear representations of Lie algebras, Lect. Notes in Math.1455, Springer-Verlag (1991), 243–271.

    Article  MathSciNet  Google Scholar 

  10. A. Nowicki,On the nonexistence of rational first integrals for systems of linear differential equations, Linear Algebra Appl. 235 (1996), 107–120.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. J. Prelle andM. F. Singer,Elementary first integrals of differential equations, Trans. Amer. Math. Soc.279 (1983), 215–229.

    Article  MATH  MathSciNet  Google Scholar 

  12. W. T. Van Horssen,On integrating factors for ordinary differential equations, Nieuw Arch. Wisk.15 (1997), 15–26.

    MATH  MathSciNet  Google Scholar 

  13. J. A. Weil,First integrals and Darboux polynomials of homogenous linear differential systems, Lect. Notes in Computer Science948, Springer-Verlag (1995), 469–484.

    MathSciNet  Google Scholar 

  14. V.E. Zakharov,What is integrability?, Springer Series in Nonlinear Dynamics, Springer-Verlag, (1991).

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, UNAM, C. Universitaria, 04510, México, D.F.

    Manuel Falconi

  2. Departament de Matemátiques, Universitat Autónoma de Barcelona, Bellaterra, 08193, Barcelona, Spain

    Jaume Llibre

Authors
  1. Manuel Falconi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jaume Llibre
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manuel Falconi.

Additional information

Dedicated to Jorge Sotomayor on his 60th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Falconi, M., Llibre, J. n-1 independent first integrals for linear differential systems in Rn and Cn . Qual. Th. Dyn. Syst 4, 233–254 (2004). https://doi.org/10.1007/BF02970860

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02970860

Key Words

Search

Navigation