Skip to main content
SpringerLink
Log in

Holonomic Systems

  • Conference paper
  • First Online:
Book cover Analytic, Algebraic and Geometric Aspects of Differential Equations

Part of the book series: Trends in Mathematics ((TM))

Abstract

New understanding of Fuchsian ordinary differential equations due to Katz and Oshima is presented. We extend it to regular holonomic systems, and proceed to global analysis by using the extended notions. Problem of constructing regular holonomic systems is also discussed.

To the memory of my mother Reiko and my father Kenkichi

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. W. Crawley-Boevey, On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero. Duke Math. J. 118, 339–352 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. P. Deligne, Équations différentielles à points singuliers réguliers. Lecture Notes in Mathematics, vol. 163 (Springer, Berlin, 1970)

    Google Scholar 

  3. M. Dettweiler, S. Reiter, An algorithm of Katz and its application to the inverse Galois problem. J. Symb. Comput. 30, 761–798 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Dettweiler, S. Reiter, Middle convolution of Fuchsian systems and the construction of rigid differential systems. J. Algebra 318, 1–24 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Gérard, A.H.M. Levelt, Étude d’une classe particulière de systèmes de Pfaff du type de Fuchs sur l’espace projectif complexe. J. Math. pures et appl. 51, 189–217 (1972)

    MathSciNet  MATH  Google Scholar 

  6. H.A. Hamm, D.T. Lê, Un théorème de Zariski du type de Lefschetz. Ann. Sci. École Norm. Sup. 6, 317–366 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  7. Y. Haraoka, Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangements. Adv. Stud. Pure Math. 62, 109–136 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Y. Haraoka, Linear differential equations in the complex domain. (Sugaku Shobo, Tokyo, 2015) (in Japanese)

    Google Scholar 

  9. Y. Haraoka, G. Filipuk, Middle convolution and deformation for Fuchsian systems. J. Lond. Math. Soc. 76, 438–450 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Y. Haraoka, S. Hamaguchi, Topological theory for Selberg type integral associated with rigid Fuchsian systems. Math. Ann. 353, 1239–1271 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Y. Haraoka, T. Kikukawa, Rigidity of monodromies for Appell’s hypergeometric functions. Opuscula Math. 35, 567–594 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. N.M. Katz, Rigid Local Systems (Princeton University Press, Princeton, NJ, 1996)

    MATH  Google Scholar 

  13. V.P. Kostov, On the Deligne-Simpson problem. Proc. Steklov Inst. Math. 238, 148–185 (2002)

    MathSciNet  MATH  Google Scholar 

  14. T. Oshima, Fractional Calculus of Weyl Algebra and Fuchsian Differential Equations. MSJ Memoirs, vol. 28 (Mathematical Society of Japan, Tokyo, 2012)

    Google Scholar 

  15. I. Shimada, Fundamental groups of complements to hypersurfaces. RIMS Kôkyûroku 1033, 27–33 (1998)

    MathSciNet  MATH  Google Scholar 

  16. E.R. van Kampen, On the fundamental group of an algebraic curve. Am. J. Math. 55, 255–260 (1933)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the JSPS grants-in-aid for scientific research B, No. 15H03628.

Author information

Authors and Affiliations

  1. Department of Mathematics, Kumamoto University, Kumamoto, 860-8555, Japan

    Yoshishige Haraoka

Authors
  1. Yoshishige Haraoka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoshishige Haraoka .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Galina Filipuk

  2. Kumamoto University, Kumamoto, Japan

    Yoshishige Haraoka

  3. Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszynski University, Warsaw, Poland

    Sławomir Michalik

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Haraoka, Y. (2017). Holonomic Systems. In: Filipuk, G., Haraoka, Y., Michalik, S. (eds) Analytic, Algebraic and Geometric Aspects of Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52842-7_2

Download citation

Publish with us

Policies and ethics

Search

Navigation