Displaying similar documents to “On vanishing inflection points of plane curves”

The dynamics of holomorphic maps near curves of fixed points

Filippo Bracci (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let M be a two-dimensional complex manifold and f : M → M a holomorphic map. Let S ⊂ M be a curve made of fixed points of f , i.e.  Fix ( f ) = S . We study the dynamics near  S in case  f acts as the identity on the normal bundle of the regular part of  S . Besides results of local nature, we prove that if  S is a globally and locally irreducible compact curve such that S · S < 0 then there exists a point p ∈ S and a holomorphic f -invariant curve with  p on the boundary which is attracted by  p under the action of  f . These results...

Local dynamics of holomorphic diffeomorphisms

Filippo Bracci (2004)

Bollettino dell'Unione Matematica Italiana

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This is a survey about local holomorphic dynamics, from Poincaré's times to nowadays. Some new ideas on how to relate discrete dynamics to continuous dynamics are also introduced. It is the text of the talk given by the author at the XVII UMI Congress at Milano.

Brolin's theorem for curves in two complex dimensions

Charles Favre, Mattias Jonsson (2003)

Annales de l’institut Fourier

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Given a holomorphic mapping f : ℙ 2 → ℙ 2 of degree d ≥ 2 we give sufficient conditions on a positive closed (1,1) current of S of unit mass under which d - n f n * S converges to the Green current as n → ∞ . We also conjecture necessary condition for the same convergence.

Some remarks on indices of holomorphic vector fields.

Marco Brunella (1997)

Publicacions Matemàtiques

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One can associate several residue-type indices to a singular point of a two-dimensional holomorphic vector field. Some of these indices depend also on the choice of a separatrix at the singular point. We establish some relations between them, especially when the singular point is a generalized curve and the separatrix is the maximal one. These local results have global consequences, for example concerning the construction of logarithmic forms defining a given holomorphic foliation. ...

Holomorphic foliations by curves on ℙ 3 with non-isolated singularities

Gilcione Nonato Costa (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let ℱ be a holomorphic foliation by curves on ℙ 3 . We treat the case where the set Sing ( ℱ ) consists of disjoint regular curves and some isolated points outside of them. In this situation, using Baum-Bott’s formula and Porteuos’theorem, we determine the number of isolated singularities, counted with multiplicities, in terms of the degree of ℱ , the multiplicity of ℱ along the curves and the degree and genus of the curves.