Displaying similar documents to “Smooth linearization of germs of R 2 -actions and holomorphic vector fields”

Local structural stability of C 2 integrable 1-forms

Alcides Lins Neto (1977)

Annales de l'institut Fourier

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In this work we consider a class of germs of singularities of integrable 1-forms in R n which are structurally stable in class C r ( r ≥ 2 if n = 3 , r ≥ 4 if n ≥ 4 ), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.

Poincaré-Hopf index and partial hyperbolicity

C. A Morales (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index 1 for vector fields with isolated zeroes in a 3 -ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.

Partial hyperbolicity and homoclinic tangencies

Sylvain Crovisier, Martin Sambarino, Dawei Yang (2015)

Journal of the European Mathematical Society

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We show that any diffeomorphism of a compact manifold can be C 1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.

Levi-flat filling of real two-spheres in symplectic manifolds (II)

Hervé Gaussier, Alexandre Sukhov (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider a compact almost complex manifold ( M , J , ω ) with smooth Levi convex boundary ∂ M and a symplectic tame form ω . Suppose that S 2 is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into ∂ M . We prove a result on filling S 2 by holomorphic discs.