Asymptotics for general connections at infinity
Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque, no. 297 (2004), pp. 189-231.
@incollection{AST_2004__297__189_0,
     author = {Simpson, Carlos},
     title = {Asymptotics for general connections at infinity},
     booktitle = {Analyse complexe, syst\`emes dynamiques, sommabilit\'e des s\'eries divergentes et th\'eories galoisiennes (II)},
     editor = {Loday-Richaud Mich\`ele},
     series = {Ast\'erisque},
     pages = {189--231},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {297},
     year = {2004},
     mrnumber = {2135666},
     zbl = {1091.34032},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2004__297__189_0/}
}
TY  - CHAP
AU  - Simpson, Carlos
TI  - Asymptotics for general connections at infinity
BT  - Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II)
AU  - Collectif
ED  - Loday-Richaud Michèle
T3  - Astérisque
PY  - 2004
SP  - 189
EP  - 231
IS  - 297
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2004__297__189_0/
LA  - en
ID  - AST_2004__297__189_0
ER  - 
%0 Book Section
%A Simpson, Carlos
%T Asymptotics for general connections at infinity
%B Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II)
%A Collectif
%E Loday-Richaud Michèle
%S Astérisque
%D 2004
%P 189-231
%N 297
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2004__297__189_0/
%G en
%F AST_2004__297__189_0
Simpson, Carlos. Asymptotics for general connections at infinity, dans Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes (II), Astérisque, no. 297 (2004), pp. 189-231. http://archive.numdam.org/item/AST_2004__297__189_0/

[1] T. Aoki, T. Kawai & Y. Takei - "On the exact steepest descent method: A new method for the description of Stokes curves", J. Math. Phys. 42 (2001), p. 3691-3713. | DOI | MR | Zbl

[2] D. Arinkin - "Orthogonality of natural sheaves on moduli stacks of S L ( 2 ) -bundles with connections on 1 minus 4 points", Selecta Math. 7 (2001), p. 213-239. | DOI | MR | Zbl

[3] D. Arinkin & S. Lysenko "On the moduli of S L ( 2 ) -bundles with connections on 1 - { x 1 , , x 4 } ", Internat. Math. Res. Notices 19 (1997), p. 983-999 | DOI | MR | Zbl

[4] R. Balian & C. Bloch "Solution of the Schrödinger equation in terms of classical paths", Ann. Physics 85 (1974), p. 514-545. | DOI | MR | Zbl

[5] C. M. Bender, M. Berry, P. Meisinger, M. Van Savage & M. Simsek - "Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians", J. Phys. A 34 (2001), no. 6, p. L31-L36. | DOI | MR | Zbl

[6] H. Berk, W. Nevins & K. Roberts - "New Stokes' line in WKB theory", J. Math. Phys. 23 (1982), p. 988-1002. | DOI | MR | Zbl

[7] L. Boutet De Monvel (ed.) - Méthodes Résurgentes: analyse algébrique des perturbations singulières, Travaux en Cours, Hermann, Paris, 1994. | MR | Zbl

[8] M. Canalis-Durand, J.-P. Ramis, R. Schäfke & Y. Sibuya - "Gevrey solutions of singularly perturbed differential equations", J. reine angew. Math. 518 (2000), p. 95-129. | MR | Zbl

[9] B. Candelpergher, J.-C. Nosmas & F. Pham - Approche de la résurgence, Actualités Mathématiques, Hermann, Paris, 1993. | MR | Zbl

[10] K.-T. Chen - "Integration of paths, geometric invariants and a generalized Baker-Hausdorff", Ann. of Math. 65 (1957), p. 163-178. | DOI | MR | Zbl

[11] O. Costin & R. Costin - "Asymptotic properties of a family of solutions of the Painlevé equation PVI", Internat. Math. Res. Notices 22 (2002), p. 1167-1182. | DOI | MR | Zbl

[12] M. Culler & P. Shalen - "Varieties of group representations and splittings of 3-manifolds", Ann. of Math. 117 (1983), p. 109-146. | DOI | MR | Zbl

[13] E. Delabaere - "Spectre de l'opérateur de Schrödinger stationnaire unidimensionnel à potentiel polynôme trigonométrique", C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), p. 807-810. | MR | Zbl

[14] E. Delabaere & H. Dillinger - "Contribution à la résurgence quantique. Résurgence de Voros et fonction spectrale de Jost", Ph.D. Thesis, Univ. Nice Sophia-Antipolis, 1991.

[15] E. Delabaere, H. Dillinger & F. Pham - "Résurgence de Voros et périodes des courbes hyperelliptiques". Ann. Inst. Fourier (Grenoble) 43 (1993), p. 163-199. | DOI | EuDML | Numdam | MR | Zbl

[16] E. Delabaere, H. Dillinger & F. Pham, "Exact semiclassical expansions for one-dimensional quantum oscillators", J. Math. Phys. 38 (1997), p. 93-132. | DOI | MR | Zbl

[17] E. Delabaere & C. Howls - "Global asymptotics for multiple integrals with boundaries", Duke Math. J. 112 (2002), p. 199-264. | DOI | MR | Zbl

[18] P. Deligne Letter to the author.

[19] R. Donagi - "Spectral covers", in Current topics in complex algebraic geometry (Berkeley, 1992/93), Math. Sci. Res. Inst. Publ., vol. 28, Cambridge Univ. Press, 1995, p. 65-86. | MR | Zbl

[20] J. Écalle - Les fonctions résurgentes. Publ. Math., Univ. d'Orsay, 1981/1985, T. I (1981), no. 81-05, | Zbl

J. Écalle - Les fonctions résurgentes. Publ. Math., Univ. d'Orsay, T. II (1981) no. 81-6, | MR

J. Écalle - Les fonctions résurgentes. Publ. Math., Univ. d'Orsay, T. III (1985), no. 85-05. See also Orsay preprint 84T 62. | MR | Zbl

[21] J. Écalle, "The acceleration operators and their applications to differential equations, quasianalytic functions, and the constructive proof of Dulac's conjecture", in Proc. ICM- 90, Kyoto, vol. II, Springer, 1991, p. 1249-1258. | MR | Zbl

[22] J. Écalle, "Singularités non abordables par la géométrie", Ann. Inst. Fourier (Grenoble) 42 (1992), p. 73-164. | DOI | EuDML | Numdam | MR | Zbl

[23] J. Écalle & B. Vallet - "Correction and linearization of resonant vector fields and diffeomorphisms", Math. Z. 229 (1998), p. 249-318. | DOI | MR | Zbl

[24] G. Gentile & V. Mastropietro - "Methods for the analysis of the Lindstedt series for KAM tori and renormalizability in classical mechanics. A review with some applications", Rev. Math. Phys. 8 (1996), p. 393-444. See also ar Xiv: chao-dyn9506004. | DOI | MR | Zbl

[25] R. Hain - "The de Rham homotopy theory of complex algebraic varieties I", K-Theory 1 (1987), p. 271-324. | DOI | MR | Zbl

[26] N. Hitchin - "Stable bundles and integrable systems", Duke Math. J. 54 (1987), p. 91-114. | DOI | MR | Zbl

[27] N. Hitchin, "The self-duality equations on a Riemann surface", Proc. London Math. Soc. 55 (1987), p. 59-126. | DOI | MR | Zbl

[28] M. Inaba, K. Iwasaki & M.-H. Saito - "Moduli of Stable Parabolic Connections, Riemann-Hilbert correspondence and Geometry of Painlevé equation of type VI". Part I. Preprint arXiv: math. AG/0309342, 2003. | Zbl

[29] S. Kamvissis - "Desingularization of a hyperelliptie curve associated with a doubly periodic Dirac potential", Bull. Greek Math. Soc. 46 (2002), p. 141-145. | EuDML | MR | Zbl

[30] V. Kanev - "Spectral curves, simple Lie algebras, and Prym-Tjurin varieties", in Theta functions - Bowdoin 1987. Part 1 (Brunswick, ME, 1987). Proc. Sympos. Pure Math., vol. 49. American Mathematical Society 1989, p. 627-645. | DOI | MR | Zbl

[31] A. Losev & Y. Manin - "New moduli spaces of pointed curves and pencils of flat connections", Michigan Math. J. 48 (2000), p. 443-472. | DOI | MR | Zbl

[32] B. Malgrange & J.-P. Ramis - "Fonctions multisommables", Ann. Inst. Fourier (Grenoble) 42 (1992), p. 353-368. | DOI | EuDML | Numdam | MR | Zbl

[33] C. Procesi - "The invariant theory of n × n matrices", Adv. in Math. 19 (1976), p. 306-381. | DOI | MR | Zbl

[34] G. Sanguinetti & N. Woodhouse - "Geometry of dual isomonodromic: deformations", Preprint, http://www.maths.ox.ac.uk/~nwoodh/dual.pdf. | DOI | Zbl

[35] C. Simpson - "A lower bound for the size of monodromy of systems of ordinary differential equations", in Algebraic geometry and analytic geometry (Tokyo, 1990), ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991, p. 198-230. | MR | Zbl

[36] C. Simpson, Asymptotic Behavior of Monodromy. Lect. Notes in Math., vol. 1502, Springer, 1991. | MR | Zbl

[37] C. Simpson, "Nonabelian Hodge theory", in Proceedings of the International Congress of Mathematicians, (Kyoto, 1990). Springer-Verlag, Tokyo, 1991, p. 198-230. | MR | Zbl

[38] C. Simpson, "Higgs bundles and local systems", Publ. Math. Inst. Hautes Etudes Sci. 75 (1992), p. 5-95. | DOI | EuDML | Numdam | MR | Zbl

[39] C. Simpson, "Moduli of representations of the fundamental group of a smooth projective variety I, II", Publ. Math. Inst. Hautes Études Sci. 79 (1994), p. 47-129, | DOI | EuDML | Numdam | MR | Zbl

C. Simpson, "Moduli of representations of the fundamental group of a smooth projective variety I, II", 80 (1994), p. 5-79. | EuDML | Numdam | MR | Zbl

[40] C. Simpson, "The Hodge filtration on nonabelian cohomology", in Algebraic geometry Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62.2, American Mathematical Society, 1997, p. 217-281. | DOI | MR | Zbl

[41] C. Stenger - "Points tournants de systèmes d'équations différentielles ordinaires singulièrement perturbées", Ph.D. Thesis, Univ. Louis Pasteur, Strasbourg, 1999, http://www-irma.u-strasbg.fr/irma/publications/1999/99019.shtml. | MR | Zbl

[42] A. Voros - "Problème spectral de Sturm-Liouville: le cas de l'oscillateur quartique", in Séminaire Bourbaki, 1982/83 vol. 602, Société Mathématique de France, 1983, p. 95-104. | EuDML | Numdam | MR | Zbl

[43] A. Voros, "The return of the quartic oscillator: the complex WKB method". Ann. Inst. H. Poincaré. Phys. Théor. 39 (1983), p. 211-338. | EuDML | Numdam | MR | Zbl

[44] A. Voros, "Résurgence quantique", Ann. Inst. Fourier (Grenoble) 43 (1993), p. 1509-1534. | DOI | EuDML | Numdam | MR | Zbl

[45] N. Woodhouse - "The symplectic and twistor geometry of the general isomonodromic deformation problem", J. Geom. Phys. 39 (2001), p. 97-128, See also the slides at http://www.maths.ox.ac.uk/~nwoodh/ini.pdf. | DOI | MR | Zbl

[46] J. Zinn-Justin - "Analyse des istantons et résultats exacts", Ann. Inst. Fourier (Grenoble) 53 (2003), p. 1259-1285. | EuDML | Numdam | MR | Zbl