Reports de recerca
Recent Submissions
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Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
(2019-06)
Research report
Open AccessWe study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional ... -
A note on symplectic and Poisson linearization of semisimple Lie algebra actions
(2015-03)
Research report
Open AccessIn this note we prove that an analytic symplectic action of a semisimple Lie algebra can be locally linearized in Darboux coordinates. This result yields simultaneous analytic linearization for Hamiltonian vector fields ... -
Action-angle variables and a KAM theorem for b-Poisson manifolds
(2015-02)
Research report
Open AccessIn this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we ... -
Xiao's conjuecture for general fibred surfaces
(2014-01-10)
Research report
Open AccessWe prove that the genus g, the relative irregularity q_f and the Clifford index c_f of a non-isotrivial fibration f satisfy the inequality q_f=g-c_f. This gives in particular a proof of Xiao’s conjecture for fibrations ... -
Stability and singularities of relative hypersurfaces
(2014-07-30)
Research report
Open AccessWe study relative hypersurfaces, and prove an instability condition for the fibres. This is the starting point for an investigation of the geometry of effective divisors on relative projective bundles. -
Algebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)
(2014-11)
Research report
Open AccessFor a class of non-hyperelliptic genus 3 curves C which are 2-fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally non-equivalent genus 2 curves whose Jacobians are degree 2 ... -
Rigidity of Poisson Lie group actions
(2014)
Research report
Open Accessn this paper we prove that close infinitesimal momentum maps associated to Poisson Lie actions are equivalent under some mild assumptions. We also obtain rigidity theorems for actual momentum maps (when the acting Lie group ... -
Lyubeznik numbers of local rings and linear strands of graded ideals
(2014-08)
Research report
Open Accessn this work we intro duce a new set of invariants asso ciated to the linear strands of a minimal free resolution of a Z -graded ideal I R = | [ x 1 ;:::;x n ] . We also prove that these invariants satisfy ... -
A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
(2014-07)
Research report
Open Access -
Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
(2014-09)
Research report
Open AccessWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider ... -
Càlcul numèric. Manual de pràctiques
(2014-07)
Research report
Open Access -
Decomposition spaces, incidence algebras and Möbius inversion
(2014-04-11)
Research report
Open Access
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