On the resolution of singularities of one-dimensional foliations on three-manifolds
- Authors: Rebelo J.C.1, Reis H.2,3
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Affiliations:
- Institut de Mathématiques de Toulouse
- Centro de Matemática da Universidade do Porto
- University of Porto
- Issue: Vol 76, No 2 (2021)
- Pages: 103-176
- Section: Articles
- URL: https://journal-vniispk.ru/0042-1316/article/view/133655
- DOI: https://doi.org/10.4213/rm9993
- ID: 133655
Cite item
Abstract
About the authors
Julio C. Rebelo
Institut de Mathématiques de Toulouse
Email: jrebelo@math.sunysb.edu
Helena Reis
Centro de Matemática da Universidade do Porto; University of Porto
References
- M. Abate, “The residual index and the dynamics of holomorphic maps tangent to the identity”, Duke Math. J., 107:1 (2001), 173–207
- В. И. Арнольд, Ю. С. Ильяшенко, “Обыкновенные дифференциальные уравнения”, Динамические системы – 1, Итоги науки и техники. Сер. Соврем. пробл. матем. Фундам. напр., 1, ВИНИТИ, М., 1985, 7–140
- М. Атья, Н. Хитчин, Геометрия и динамика магнитных монополей, Мир, М., 1991, 150 с.
- F. E. Brochero Martinez, F. Cano, L. Lopez-Hernanz, “Parabolic curves for diffeomorphisms in $mathbb{C}^2$”, Publ. Mat., 52:1 (2008), 189–194
- C. Camacho, A. Lins Neto, P. Sad, “Topological invariants and equidesingularization for holomorphic vector fields”, J. Differential Geom., 20:1 (1984), 143–174
- C. Camacho, P. Sad, “Invariant varieties through singularities of holomorphic vector fields”, Ann. of Math. (2), 115:3 (1982), 579–595
- F. Cano, “Reduction of the singularities of codimension one singular foliations in dimension three”, Ann. of Math. (2), 160:3 (2004), 907–1011
- F. Cano, C. Roche, “Vector fields tangent to foliations and blow-ups”, J. Singul., 9 (2014), 43–49
- F. Cano, C. Roche, M. Spivakovsky, “Reduction of singularities of three-dimensional line foliations”, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 108:1 (2014), 221–258
- F. Cano Torres, Desingularization strategies for three-dimensional vector fields, Lecture Notes in Math., 1259, Springer-Verlag, Berlin, 1987, x+194 pp.
- R. Conte (ed.), The Painleve property. One century later, CRM Ser. Math. Phys., Springer-Verlag, New York, 1999, xxvi+810 pp.
- G. Dloussky, K. Oeljeklaus, M. Toma, “Surfaces de la classe $mathrm{VII}_0$ admettant un champ de vecteurs”, Comment. Math. Helv., 75:2 (2000), 255–270
- П. М. Елизаров, Ю. С. Ильяшенко, “Замечания об орбитальной аналитической классификации ростков векторных полей”, Матем. сб., 121(163):1(5) (1983), 111–126
- А. Э. Еременко, “Мероморфные решения алгебраических дифференциальных уравнений”, УМН, 37:4(226) (1982), 53–82
- E. Ghys, J. C. Rebelo, “Singularites des flots holomorphes. II”, Ann. Inst. Fourier (Grenoble), 47:4 (1997), 1117–1174
- A. Guillot, “Sur les equations d'Halphen et les actions de $operatorname{SL}_2(mathbf C)$”, Publ. Math. Inst. Hautes Etudes Sci., 105:1 (2007), 221–294
- A. Guillot, “The geometry of Chazy's homogeneous third-order differential equations”, Funkcial. Ekvac., 55:1 (2012), 67–87
- A. Guillot, J. C. Rebelo, “Semicomplete meromorphic vector fields on complex surfaces”, J. Reine Angew. Math., 2012:667 (2012), 27–65
- M. Hakim, Transformations tangent to the identity. Stable pieces of manifolds, Prepublication Orsay 97-30, Univ. de Paris-Sud, Orsay, 1997, 36 pp.
- M. Hakim, “Analytic transformations of $(mathbf{C}^p,0)$ tangent to the identity”, Duke Math. J., 92:2 (1998), 403–428
- Yu. Ilyashenko, S. Yakovenko, Lectures on analytic differential equations, Grad. Stud. Math., 86, Amer. Math. Soc., Providence, RI, 2008, xiv+625 pp.
- E. L. Ince, Ordinary differential equations, Reprint of the 1st ed., Dover Publications, New York, 1956, viii+558 pp.
- J. Malmquist, “Sur l'etude analytique des solutions d'un système d'equations differentielles dans le voisinage d'un point singulier d'indetermination. I”, Acta Math., 73 (1941), 87–129
- F. Martin, E. Royer, “Formes modulaires et periodes”, Formes modulaires et transcendance, Semin. Congr., 12, Soc. Math. France, Paris, 2005, 1–117
- J.-F. Mattei, R. Moussu, “Holonomie et integrales premières”, Ann. Sci. Ecole Norm. Sup. (4), 13:4 (1980), 469–523
- M. McQuillan, D. Panazzolo, “Almost etale resolution of foliations”, J. Differential Geometry, 95:2 (2013), 279–319
- D. Panazzolo, “Resolution of singularities of real-analytic vector fields in dimension three”, Acta Math., 197:2 (2006), 167–289
- O. Piltant, “An axiomatic version of Zariski's patching theorem”, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 107:1 (2013), 91–121
- J.-P. Ramis, Y. Sibuya, “Hukuhara domains and fundamental existence and uniqueness theorems for asymptotic solutions of Gevrey type”, Asymptotic Anal., 2:1 (1989), 39–94
- J. C. Rebelo, “Singularites des flots holomorphes”, Ann. Inst. Fourier (Grenoble), 46:2 (1996), 411–428
- H. Reis, “Equivalence and semi-completude of foliations”, Nonlinear Anal., 64:8 (2006), 1654–1665
- H. Reis, “Semi-complete vector fields of saddle-node type in $mathbb C^n$”, Trans. Amer. Math. Soc., 360:12 (2008), 6611–6630
- A. Seidenberg, “Reduction of singularities of the differential equation $A dy=B dx$”, Amer. J. Math., 90 (1968), 248–269
- B. J. Weickert, “Attracting basins for automorphisms of $mathbf{C}^2$”, Invent. Math., 132:3 (1998), 581–605
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