Reports de recerca: Recent submissions
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Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type
(201402)
External research report
Open AccessWe study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2dimensional torus with ... 
Generalized CliffordSeveri inequality and the volume of irregular varieties
(20130302)
External research report
Restricted access  author's decisionWe give a sharp lower bound for the selfintersection of a nef li ne bundle L on an irregular variety X in terms of its continuous global sections and the Albanese dim ension of X, which we call the Generalized CliffordSeveri ... 
Local description of phylogenetic groupbased models
(201312)
External research report
Open AccessMotivated by phylogenetics, our aim is to obtain a system of equations that de ne a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties de ... 
Testing of the three multiplicatively closed (Lie Markov) model heirarchies which respect purine/pyrimidine, WatsonCrick, and amino/keto nucleotide groupings
(201403)
External research report
Restricted access  confidentiality agreementWe present three hierarchies of Lie Markov models of DNA sequence evolution. These models are (locally) “multiplicatively closed,” meaning that the composition of two Markov matrices in the model results, with some (rare) ... 
Lie Markov models with purine/pyrimidine symmetry
(201306)
External research report
Open AccessContinuoustime Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying timeindependent rates of substitutions between states in the chain. In applications, ... 
Periodic orbits of planar integrable birational maps
(20140214)
External research report
Open AccessA birational planar map F possessing a rational ﬁrst integral preserves a foliation of the plane given by algebraic curves which, if F is not globally periodic, is given by a foliation of curves that have generically ... 
Symplectic topology of bsymplectic manifolds
(201312)
External research report
Open AccessA Poisson manifold (M2n; ) is bsymplectic if Vn is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to bsymplectic manifolds. The ... 
An extension problem for the CR fractional Laplacian
(201312)
External research report
Open AccessWe show that the conformally invariant fractional powers of the subLaplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this ... 
Singularities for a fully nonlinear elliptic equation in conformal geometry
(201308)
External research report
Open AccessWe construct some radially symmetric solutions of the constant k equation on R n n R p , which blow up exactly at the submanifold R p R n . These are the basic models to the problem of nding complete metrics ... 
Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion
(201306)
External research report
Open AccessAbstract. We consider models given by Hamiltonians of the form H ( I;';p;q;t ; " ) = h ( I )+ n X j =1 1 2 p 2 j + V j ( q j ) + "Q ( I;';p;q;t ; " ) where I 2I R d ;' 2 T d ... 
Toric actions on bsymplectic manifolds
(2013)
External research report
Open AccessWe study Hamiltonian actions on bsymplectic manifolds with a focus on the e ective case of half the dimension of the manifold. In particular, we prove a Delzanttype theorem that classi es these manifolds using polytopes ... 
Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies
(2013)
External research report
Open AccessWe study the splitting of invariant manifolds of whiskered t ori with two or three frequencies in nearlyintegrable Hamiltonian systems. We consider 2dimensional tori with a frequency vector ω = (1 , Ω) where Ω is ...