Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation

Shun Shimomura

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2000)

  • Volume: 29, Issue: 1, page 1-17
  • ISSN: 0391-173X

How to cite

top

Shimomura, Shun. "Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 29.1 (2000): 1-17. <http://eudml.org/doc/84403>.

@article{Shimomura2000,
author = {Shimomura, Shun},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {singularities; Schlesinger system; degenerate Garnier system; Painlevé property},
language = {eng},
number = {1},
pages = {1-17},
publisher = {Scuola normale superiore},
title = {Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation},
url = {http://eudml.org/doc/84403},
volume = {29},
year = {2000},
}

TY - JOUR
AU - Shimomura, Shun
TI - Painlevé property of a degenerate Garnier system of (9/2)-type and of a certain fourth order non-linear ordinary differential equation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2000
PB - Scuola normale superiore
VL - 29
IS - 1
SP - 1
EP - 17
LA - eng
KW - singularities; Schlesinger system; degenerate Garnier system; Painlevé property
UR - http://eudml.org/doc/84403
ER -

References

top
  1. [1] H. Flaschka - A.C. Newell, Monodromy- and spectrum-preserving deformations I, Comm. Math. Phys.76 (1980), 65-116. Zbl0439.34005MR588248
  2. [2] R. Fuchs, Über lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegene wesentlich singulären Stellen, Math. Ann.63 (1907), 301-321. Zbl38.0362.01MR1511408JFM38.0362.01
  3. [3] R. Garnier, Sur des équations différentielles du troisième ordre dont l'intégrale générale est uniforme et sur une classe d'équations nouvelles d'ordre supérieur dont l'intégrale générale a ses points critiques fixes, Ann. Sci. École Norm. Sup.29 (1912), 1-126. Zbl43.0382.01MR1509146JFM43.0382.01
  4. [4] K. Iwasaki - H. Kimura - S. Shimomura - M. Yoshida, "From Gauss to Painlevé, A Modern Theory of Special Functions ", Vieweg, Braunschweig, 1991. Zbl0743.34014MR1118604
  5. [5] M. Jimbo - T. Miwa - K. Ueno, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients, I, — General theory and τ-function —, Phys. D2 (1981), 306-352. Zbl1194.34167
  6. [6] M. Jimbo - T. Miwa, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients, II, Phys. D2 (1981), 407-448. Zbl1194.34166MR625446
  7. [7] H. Kimura, The degeneration of the two dimensional Garnier system and the polynomial Hamiltonian structure, Ann. Mat. Pura Appl.155 (1989), 25-74. Zbl0693.34043MR1042827
  8. [8] H. Kimura - K. Okamoto, On the polynomial Hamiltonian structure of the Garnier system, J. Math. Pures Appl. 63 (1984), 129-146. Zbl0562.34004MR776915
  9. [9] B. Malgrange, "Sur les déformations isomonodromiques, I: Singularités régulières", Séminaire de l'École Norm. Sup., Birkhäuser, 1982. Zbl0528.32017MR728431
  10. [10] T. Miwa, Painlevé property of monodromy preserving deformation equations and the analyticity of τ -functions, Publ. Res. Inst. Math. Sci.17 (1981), 703-721. Zbl0605.34005
  11. [11] M. Noumi - Y. Yamada, Higher order Painlevé equations of type Al (1), Funkcial. Ekvac. 41 (1998), 483-503. Zbl1140.34303MR1676885
  12. [12] M. Noumi - Y. Yamada, private communication. 
  13. [13] K. Okamoto, Isomonodromic deformation and Painleve equations, and the Garnier system, J. Fac. Sci. Univ. Tokyo Sect. IA Math.33 (1986), 575-618. Zbl0631.34011MR866050
  14. [14] L. Schlesinger, Über eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten, J. Reine Angew. Math.141 (1912), 96-145. Zbl43.0385.01JFM43.0385.01
  15. [15] K. Ueno, Monodromy preserving deformation of linear differential equations with irregular singular points, Proc. Japan Acad. Ser. A Math. Sci.56 (1980), 97-102. Zbl0487.34004MR575985

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.