Now showing items 13-24 of 102

  • Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type 

    Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (2014-02)
    External research report
    Open Access
    We 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 2-dimensional torus with ...
  • Generalized Clifford-Severi inequality and the volume of irregular varieties 

    Barja Yáñez, Miguel Ángel (2013-03-02)
    External research report
    Restricted access - author's decision
    We 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 Clifford-Severi ...
  • Local description of phylogenetic group-based models 

    Casanellas Rius, Marta; Fernández Sánchez, Jesús; Michalek, Mateusz (2013-12)
    External research report
    Open Access
    Motivated 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, Watson-Crick, and amino/keto nucleotide groupings 

    Woodhams, Michael D.; Fernández Sánchez, Jesús; Sumner, Jeremy (2014-03)
    External research report
    Restricted access - confidentiality agreement
    We 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 

    Fernández Sánchez, Jesús; Sumner, Jeremy; Jarvis, Peter; Woodhams, Michael D. (2013-06)
    External research report
    Open Access
    Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, ...
  • Periodic orbits of planar integrable birational maps 

    Gálvez Carrillo, Maria Immaculada; Mañosa Fernández, Víctor (2014-02-14)
    External research report
    Open Access
    A 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 b-symplectic manifolds 

    Miranda Galcerán, Eva; Martinez Torres, David; Frejlich, Pedro (2013-12)
    External research report
    Open Access
    A Poisson manifold (M2n; ) is b-symplectic if Vn is transverse to the zero section. In this paper we apply techniques of Symplectic Topology to address global questions pertaining to b-symplectic manifolds. The ...
  • An extension problem for the CR fractional Laplacian 

    Frank, Rupert L.; González Nogueras, María del Mar; Monticelli, Dario D.; Tan, Jinggang (2013-12)
    External research report
    Open Access
    We show that the conformally invariant fractional powers of the sub-Laplacian 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 non-linear elliptic equation in conformal geometry 

    González Nogueras, María del Mar; Mazzieri, Lorenzo (2013-08)
    External research report
    Open Access
    We 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 

    Delshams Valdés, Amadeu; de la Llave, Rafael; Martínez-Seara Alonso, M. Teresa (2013-06)
    External research report
    Open Access
    Abstract. 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 b-symplectic manifolds 

    Miranda Galcerán, Eva; Pires, Ana Rita; Guillemin, Victor; Scott, Geoffrey (2013)
    External research report
    Open Access
    We study Hamiltonian actions on b-symplectic manifolds with a focus on the e ective case of half the dimension of the manifold. In particular, we prove a Delzant-type 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 

    Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (2013)
    External research report
    Open Access
    We study the splitting of invariant manifolds of whiskered t ori with two or three frequencies in nearly-integrable Hamiltonian systems. We consider 2-dimensional tori with a frequency vector ω = (1 , Ω) where Ω is ...