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Book Information:
Author:
H. Zoladek
Title:
The monodromy group
Additional book information:
Birkhäuser,
Basel-Boston-Berlin,
2006,
xi+ 580 pp.,
ISBN 978-3-7643-7535-5,
US$129.00$
D. V. Anosov and A. A. Bolibruch, The Riemann-Hilbert problem, Aspects of Mathematics, E22, Friedr. Vieweg & Sohn, Braunschweig, 1994. MR 1276272, DOI 10.1007/978-3-322-92909-9
V. I. Arnol′d, S. M. Guseĭn-Zade, and A. N. Varchenko, Singularities of differentiable maps. Vol. I, Monographs in Mathematics, vol. 82, Birkhäuser Boston, Inc., Boston, MA, 1985. The classification of critical points, caustics and wave fronts; Translated from the Russian by Ian Porteous and Mark Reynolds. MR 777682, DOI 10.1007/978-1-4612-5154-5
V. I. Arnol′d, S. M. Guseĭn-Zade, and A. N. Varchenko, Singularities of differentiable maps. Vol. II, Monographs in Mathematics, vol. 83, Birkhäuser Boston, Inc., Boston, MA, 1988. Monodromy and asymptotics of integrals; Translated from the Russian by Hugh Porteous; Translation revised by the authors and James Montaldi. MR 966191, DOI 10.1007/978-1-4612-3940-6
A. A. Bolibruch, S. Malek, and C. Mitschi, On the generalized Riemann-Hilbert problem with irregular singularities, Expo. Math. 24 (2006), no. 3, 235–272. MR 2250948, DOI 10.1016/j.exmath.2005.11.003
Jean Écalle, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1992 (French, with French summary). MR 1399559
A. I. Gladyshev, On the Riemann-Hilbert problem in dimension 4, J. Dynam. Control Systems 6 (2000), no. 2, 219–264. MR 1746973, DOI 10.1023/A:1009582120446
Xavier Gómez-Mont, The transverse dynamics of a holomorphic flow, Ann. of Math. (2) 127 (1988), no. 1, 49–92. MR 924673, DOI 10.2307/1971416
Yu. S. Il′yashenko, Finiteness theorems for limit cycles, Translations of Mathematical Monographs, vol. 94, American Mathematical Society, Providence, RI, 1991. Translated from the Russian by H. H. McFaden. MR 1133882, DOI 10.1090/mmono/094
Yu. S. Il′yashenko, Nonlinear Stokes phenomena, Nonlinear Stokes phenomena, Adv. Soviet Math., vol. 14, Amer. Math. Soc., Providence, RI, 1993, pp. 1–55. MR 1206041, DOI 10.1016/j.cnsns.2015.04.003
Yu. S. Il′yashenko and A. G. Khovanskiĭ, Galois groups, Stokes operators and a theorem of Ramis, Funktsional. Anal. i Prilozhen. 24 (1990), no. 4, 31–42, 96 (Russian); English transl., Funct. Anal. Appl. 24 (1990), no. 4, 286–296 (1991). MR 1092801, DOI 10.1007/BF01077333
[IYa] Yu. Ilyashenko and S. Yakovenko, Lectures on Analytic Differential Equations, in preparation.
A. G. Khovanskiĭ, Fewnomials, Translations of Mathematical Monographs, vol. 88, American Mathematical Society, Providence, RI, 1991. Translated from the Russian by Smilka Zdravkovska. MR 1108621, DOI 10.1090/mmono/088
Alcides Lins Neto, Construction of singular holomorphic vector fields and foliations in dimension two, J. Differential Geom. 26 (1987), no. 1, 1–31. MR 892029
Frank Loray and Julio C. Rebelo, Minimal, rigid foliations by curves on $\Bbb C\Bbb P^n$, J. Eur. Math. Soc. (JEMS) 5 (2003), no. 2, 147–201. MR 1985614, DOI 10.1007/s10097-002-0049-6
Jean-François Mattei and Eliane Salem, Complete systems of topological and analytical invariants for a generic foliation of $(\textbf {C}^2,0)$, Math. Res. Lett. 4 (1997), no. 1, 131–141. MR 1432816, DOI 10.4310/MRL.1997.v4.n1.a12
- [AB]
- D.V. Anosov and A.A. Bolibruch, The Riemann-Hilbert problem, Aspects of Mathematics, E22 Friedr. Vieweg & Sohn, Braunschweig, 1994. MR 1276272
- [AGV1]
- V.I. Arnold, S.M. Gusein-Zade, and A.N. Varchenko, Singularities of differentiable maps. Vol. I. The classification of critical points, caustics and wave fronts, Translated from the Russian by Ian Porteous and Mark Reynolds, Monographs in Mathematics, vol. 82, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 0777682
- [AGV2]
- V.I. Arnold, S.M. Gusein-Zade, and A.N. Varchenko, Singularities of differentiable maps. Vol. II. Monodromy and asymptotics of integrals, Translated from the Russian by Hugh Porteous. Translation revised by the authors and James Montaldi, Monographs in Mathematics, vol. 83, Birkhäuser Boston, Inc., Boston, MA, 1988. MR 0966191
- [BMM]
- A.A. Bolibruch, S. Malek, and C. Mitschi, On the generalized Riemann-Hilbert problem with irregular singularities, Expo. Math. 24, no. 3 (2006), 235-272. MR 2250948
- [E]
- J. Écalle, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac (French) [Introduction to analyzable functions and constructive proof of the Dulac conjecture], Actualites Mathematiques [Current Mathematical Topics], Hermann, Paris, 1992. MR 1399559
- [G]
- A.I. Gladyshev, On the Riemann-Hilbert problem in dimension 4, J. Dynam. Control Systems 6, no. 2 (2000), 219-264. MR 1746973
- [G-M]
- X. Gomez-Mont, The transverse dynamics of a holomorphic flow, Ann. of Math. (2) 127, no. 1 (1988), 49-92. MR 0924673
- [I1]
- Yu. Ilyashenko, Finiteness Theorems for Limit Cycles, American Mathematical Society, Providence, RI, 1991. MR 1133882
- [I2]
- Yu.S. Ilyashenko, editor, Nonlinear Stokes Phenomena, Adv. Soviet Math., vol. 14, Amer. Math. Soc, Providence, RI, 1993. MR 1206041
- [IKh]
- Yu. Ilyashenko and A. Khovanski, Galois groups, Stokes operators and Ramis theorem, Funct. Anal. and Appl 4, no. 3 (1990), 31-42. MR 1092801
- [IYa]
- Yu. Ilyashenko and S. Yakovenko, Lectures on Analytic Differential Equations, in preparation.
- [Kh]
- A.G. Khovanski, Fewnomials, Translated from the Russian by Smilka Zdravkovska, Translations of Mathematical Monographs, vol. 88, American Mathematical Society, Providence, RI, 1991. MR 1108621
- [L-N]
- A. Lins-Neto, Construction of singular holomorphic vector fields and foliations in dimension two, J. Differential Geom. 26 (1987), 1-31. MR 0892029
- [LR]
- F. Loray and J.C. Rebelo, Minimal, rigid foliations by curves on
, J. Eur. Math. Soc. (JEMS) 5, no. 2 (2003), 147-201. MR 1985614
- [MS]
- J-F. Mattei and E. Salem, Complete systems of topological and analytical invariants for a generic foliation of
, Math. Res. Lett. 4, no. 1 (1997), 131-141. MR 1432816
Review Information:
Reviewer:
Yulij Ilyashenko
Affiliation:
Cornell University; Moscow State and Independent Universities, Steklov Institute
Email:
yulij@math.cornell.edu
Journal:
Bull. Amer. Math. Soc.
45 (2008), 329-334
DOI:
https://doi.org/10.1090/S0273-0979-07-01165-2
Published electronically:
June 22, 2007
Review copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
