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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)

- É. Ghys, X. Gómez-Mont, J. Saludes
- 2001

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)

- H.-Ch Graf Von Bothmer, W Ebeling, X Gómez-Mont
- 2008

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)

- PAVAO MARDEŠIĆ, Xavier Gómez-Mont, Luis Giraldo
- 2013

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)

- Ch Bonatti, X Gómez-Mont, R Vila-Freyer
- 2008

We introduce the geodesic flow on the leaves of a holomorphic foliation with leaves of dimension 1 and hyperbolic, corresponding to the unique complete metric of curvature-1 compatible with its conformal structure. We do these for the foliations associated to Riccati equations, which are the projectivisation of the solutions of a linear ordinary… (More)

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