A Theorem of Versality for Unfoldings of Complex Analytic Foliation Singularities.
Tatsuo Suwa (1981/82)
Inventiones mathematicae
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Tatsuo Suwa (1981/82)
Inventiones mathematicae
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Gabriel Calsamiglia, Bertrand Deroin, Sidney Frankel, Adolfo Guillot (2013)
Journal of the European Mathematical Society
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In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty...
B. Scárdua (2003)
Fundamenta Mathematicae
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We study the group Aut(ℱ) of (self) isomorphisms of a holomorphic foliation ℱ with singularities on a complex manifold. We prove, for instance, that for a polynomial foliation on ℂ² this group consists of algebraic elements provided that the line at infinity ℂP(2)∖ℂ² is not invariant under the foliation. If in addition ℱ is of general type (cf. [20]) then Aut(ℱ) is finite. For a foliation with hyperbolic singularities at infinity, if there is a transcendental automorphism then the foliation...
C. Bonatti (1993)
Ensaios Matemáticos
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Scorpan, Alexandru (2003)
Algebraic & Geometric Topology
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Igor Nikolaev (1996)
Annales de l'institut Fourier
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Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.
Richard Sacksteder (1975)
Annales de l'institut Fourier
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The author gives an example showing that Thurston’s stability theorem cannot be generalized to non-oriented foliations.
Felipe Cano (1998)
Banach Center Publications
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Hiromichi Nakayama (1991)
Annales de l'institut Fourier
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We consider transversely affine foliations without compact leaves of higher genus surface bundles over the circle of pseudo-Anosov type such that the Euler classes of the tangent bundles of the foliations coincide with that of the bundle foliation. We classify such foliations of those surface bundles whose monodromies satisfy a certain condition.
Robert Wolak (1985)
Annales Polonici Mathematici
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Rufus Bowen (1975)
Publications mathématiques et informatique de Rennes
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Carlo Petronio (1999)
Rendiconti del Seminario Matematico della Università di Padova
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