Available in electronic format
Available in print format		 Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues: 1891 - Present
Previous Article | Next Article
     

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF DVI PostScript

Book Information

Author(s): V. I. Gromak, I. Laine and S. Shimomura
Title: Painleve differential equations in the complex plane
Additional book information: de Gruyter Studies in Mathematics, volume 28, Walter de Gruyter, Berlin, 2002, viii + 303, $89.95, 3-11-017379-4

References:

[B]
L. Bieberbach, Theorie der gewöhnlichen Differentialgleichungen, Springer, 1965. MR 31:408
[B1]
P. Boutroux, Sur quelques propriétés des fonctions entières, Acta. Math. 28 (1904), 97-224.
[B2]
P. Boutroux, Recherches sur les transcendentes de M. Painlevé et l'étude asymptotique des équations différentielles du seconde ordre, Ann. École Norm. Supér. 30 (1913), 255-375; and Ann. École Norm. Supér. 31 (1914), 99-159.
[HL1]
A. Hinkkanen, I. Laine, Solutions of the first and second Painlevé equations are meromorphic, Journal d'Analyse Math. 79 (1999), 345-377. MR 2001d:34149
[HL2]
A. Hinkkanen, I. Laine, Solutions of a modified third Painlevé equation are meromorphic, Journal d'Analyse Math. 85 (2001), 323-337. MR 2003i:34199
[HL3]
A. Hinkkanen, I. Laine, Solutions of a modified fifth Painlevé equation are meromorphic, Report Univ. Jyväskylä 83 (2001), 133-146. MR 2003a:34153
[I]
E.L. Ince, Ordinary differential equations, Dover Publ., 1956. MR 6:65f
[P1]
P. Painlevé, Mémoire sur les équations différentielles dont l'intégrale générale est uniforme, Bull. Soc. Math. France 28 (1900), 201-261.
[P2]
P. Painlevé, Sur les équations différentielles du second ordre et d'ordre supérieur, dont l'intégrale générale est uniforme, Acta Math. 25 (1902), 1-86.
[Sh]
S. Shimomura, Growth of the first, the second and the fourth Painlevé transcendents, Math. Proc. Cambr. Philos. Soc. 134 (2003), 259-269. MR 2004a:34175
[St1]
N. Steinmetz, On Painlevé's equations I, II, and IV, Journal d'Analyse Math. 82 (2000), 363-377. MR 2002d:34157
[St2]
N. Steinmetz, Value distribution of the Painlevé transcendents, Israel J. Math. 128 (2002), 29-52. MR 2003c:34152
[W]
H. Wittich, Eindeutige Lösungen der Differentialgleichungen $w''= P(z,w),$ Math. Ann. 125 (1953), 355-365. MR 14:873e

Additional Information:

Reviewer(s):
Norbert Steinmetz
Affiliation: University of Dortmund
Email: stein@math.uni-dortmund.de

Review Information:
Journal: Bull. Amer. Math. Soc. 41 (2004), 523-528.

MSC (2000): Primary 34M05, 34M55, 30D35
DOI: 10.1090/S0273-0979-04-01017-1
PII: S 0273-0979(04)01017-1
Posted: March 24, 2004
Copyright of article: Copyright 2004, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google