X. Gómez-Mont

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We propose a geometric sufficient criterium " ` a la Furstenberg " for the existence of non-zero Lyapunov exponents for certain linear cocycles over hyperbolic transformations: non-existence of probability measures on the fibers invariant under the cocycle and under the holonomies of the stable and unstable foliations of the transformation. This criterium(More)
In this paper we study foliations F on compact manifolds M , of real codimen-sion 2, with a transversal holomorphic structure. We construct a decomposition of M into dynamically defined components, similar to the Fatou/Julia sets for iteration of rational functions, or the region of discontinuity/limit set partition for Kleinian groups in P SL(2, C). All(More)
Let (V, 0) be a germ of a complete intersection variety in C n+k , n > 0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on C n+k tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient(More)
Gómez-Mont, Seade and Verjovsky introduced an index , now called GSV-index, generalizing the Poincaré-Hopf index to complex vector fields tangent to singular hypersurfaces. The GSV-index extends to the real case. This is a survey paper on the joint research with Gómez-Mont and Giraldo about calculating the GSV-index Ind V±,0 (X) of a real vector field X(More)
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