C k -conjugacy of holomorphic flows near a singularity

Marc Chaperon

Publications Mathématiques de l'IHÉS (1986)

  • Volume: 64, page 143-183
  • ISSN: 0073-8301

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Chaperon, Marc. "$C^k$-conjugacy of holomorphic flows near a singularity." Publications Mathématiques de l'IHÉS 64 (1986): 143-183. <http://eudml.org/doc/104015>.

@article{Chaperon1986,
author = {Chaperon, Marc},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {germ of a holomorphic vector field; S-normal form; Poincaré domain; Siegel domain; Holomorphic conjugacy; -conjugacy; hyperbolic; weakly hyperbolic},
language = {eng},
pages = {143-183},
publisher = {Institut des Hautes Études Scientifiques},
title = {$C^k$-conjugacy of holomorphic flows near a singularity},
url = {http://eudml.org/doc/104015},
volume = {64},
year = {1986},
}

TY - JOUR
AU - Chaperon, Marc
TI - $C^k$-conjugacy of holomorphic flows near a singularity
JO - Publications Mathématiques de l'IHÉS
PY - 1986
PB - Institut des Hautes Études Scientifiques
VL - 64
SP - 143
EP - 183
LA - eng
KW - germ of a holomorphic vector field; S-normal form; Poincaré domain; Siegel domain; Holomorphic conjugacy; -conjugacy; hyperbolic; weakly hyperbolic
UR - http://eudml.org/doc/104015
ER -

References

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  1. [A] V. I. ARNOL'D, Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Moscou, Mir, 1980. Zbl0455.34001MR83a:34003
  2. [C] C. CAMACHO, On Rk X Zl-actions, in Differentiable Dynamical Systems, M. M. PEIXOTO ed., IMPA, Academic Press, 1973. Zbl0274.58006MR51 #11585
  3. [CKP] C. CAMACHO, N. KUIPER, J. PALIS, The topology of holomorphic flows with singularity, Publ. Math. I.H.E.S., 48 (1978), 5-38. Zbl0411.58018MR80j:58045
  4. [Ch 8o] M. CHAPERON, Propriétés génériques des germes d'actions différentiables de groupes de Lie commutatifs élémentaires, thèse, Université Paris 7, 1980. 
  5. [Ch 85] M. CHAPERON, Differential geometry and dynamics : two examples, in Singularities and Dynamical Systems, S. N. PNEVMATIKOS ed., Elsevier B. V. (North Holland), 1985, 187-207. Zbl0576.57029MR86k:58100
  6. [Ch 86] M. CHAPERON, Géométrie différentielle et singularités de systèmes dynamiques, Astérisque, 138-139 (1986). Zbl0601.58002MR88h:58039
  7. [Ch 86a] M. CHAPERON, Invariant manifolds and a preparation lemma for complex flows near a singularity, Preprint, École, Polytechnique, 1986. 
  8. [Ch 86b] M. CHAPERON, Ck-versal unfoldings of holomorphic flows near their singularities, Preprint, École Polytechnique 1986. 
  9. [Ch 86c] M. CHAPERON, C1-linearisable local holomorphic flows, to appear. 
  10. [Ch 86d] M. CHAPERON, Smooth conjugacy results for germs of smooth Zk X Rm-actions preserving various structures, to appear. 
  11. [CZ] C. C. CONLEY, E. ZEHNDER, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnol'd, Invent. Math., 73 (1983), 33-49. Zbl0516.58017MR85e:58044
  12. [DR] F. DUMORTIER, R. ROUSSARIE, Smooth linearisation of germs of R2-actions and holomorphic vector fields, Ann. Inst. Fourier, 30 (1) (1980), 31-64. Zbl0418.58015MR81k:58060
  13. [G] J. GUCKENHEIMER, Hartman's theorem for complex flows in the Poincaré domain, Composition Math., 24 (1) (1972). Zbl0239.58007MR46 #920
  14. [I] Ju. S. Il'IAŠENKO, Global and local aspects of the theory of complex differential equations, Proceedings of the International Congress of Mathematicians, Helsinki, 1978, 821-826. Zbl0434.34003
  15. [LM] S. LÓPEZ DE MEDRANO, Topology of the intersection of quadrics in Rn, Preprint, Universidad Nacional Autónoma de Mexico, 1986. Zbl0681.57020
  16. [MR] J. MARTINET, J. P. RAMIS, Problèmes de modules pour des équations différentielles non linéaires du premier ordre, Publ. Math. I.H.E.S., 55 (1982), 63-164. Zbl0546.58038MR84k:34011
  17. [N] E. NELSON, Topics in dynamics, Part I, Flows, Princeton, 1970. Zbl0197.10702

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