Resonant confluence of singular points and stokes phenomena

Journal of Dynamical and Control Systems

Volumn 10, Issue 2, 2004, Pages 253-302

  Glutsyuk, A A ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

Confluence; Fuchsian singularity; Linear ordinary differential equations with complex time; Monodromy; Resonant irregular singularity; Stokes operators

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES;

FUCHSIAN SINGULARITY; LINEAR ORDINARY DIFFERENTIAL EQUATIONS; MONODROMY; RESONANT CONFLUENCE; RESONANT IRREGULAR SINGULARITY; STOKES OPERATORS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 3943050052     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JODS.0000024125.05337.9e     Document Type: Article

References (14)

1. V. I. Arnold and Yu. S. Ilyashenko, Ordinary differential equations. In: Progress in Science and Technology, Series on Contemporary Problems in Mathematics, Fundamental Directions [in Russian], Dynamical Systems-1. All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1985).
2. W. Balser, W. B. Jurkat, and D. A. Lutz, Birkhoff invariants and Stokes' multipliers for meromorphic linear differential equations. J. Math. Anal. Appl. 71 (1979), No. 1, 48-94.
3. A. Duval, Biconfluence et groupe de Galois. J. Fac. Sci. Tokyo, Sect. IA, Math. 38 (1991), No. 2, 211-223.
4. R. Garnier, Sur les singularités irreguliéres des equations differentielles linéaires. J. Math. Pures Appl. 2 (1919 ), 99-198.
5. A. Glutsyuk, Stokes operators via limit monodromy of generic perturbation. J. Dynam. Control Systems 5 (1999), No. 1, 101-135.
6. A. Glutsyuk, Confluence of singular points and the nonlinear Stokes phenomena. Tr. Mos. Mat. Obshch. 62 (2001), 54-104.
7. Yu. S. Ilyashenko, Nonlinear Stokes Phenomena. Adv. Sov. Math. 14 (1993).
8. W. B. Jurkat, D. A. Lutz, and A. Peyerimhoff, Birkhoff invariants and effective calculations for meromorphic linear differential equations. J. Math. Anal. Appl. 53 (1976), No. 2, 438-470.
9. W. B. Jurkat, D. A. Lutz, and A. Peyerimhoff, Birkhoff invariants and effective calculations for meromorphic linear differential equations. Houston J. Math. 2 (1976), No. 2, 207-238.
10. J. Martinet, Remarques sur la bifurcation noeud-col dans le domaine complexe. Astérisque, 150-151 (1987), 131-149.
11. J .Martinet and J.-P. Ramis, Problèmes de modules pour des équations différentielles non linéaires du premier ordre. Inst. Hautes Études Sci. Publ. Math. 55 (1982), 63-164.
12. J.-P. Ramis, Confluence et resurgence. J. Fac. Sci. Tokyo, Sect. IA, Math. 36 (1989), No. 3, 703-716.
13. Y. Sibuya, Stokes phenomena. Bull. Amer. Math. Soc. 83 (1977), 1075-1077.
14. C. Zhang, Quelques études en théorie des équations fonctionnelles et en analyse combinatoire. Thése 1994. Institut de Recherche Mathematique Avancée, Univ. Louis Pasteur et CNRS