Now showing items 1-7 of 7

  • Adiabatic invariant of the harmonic oscillator, complex matching and resurgence 

    Bonet Revés, Carles; Sauzin, D.; Martínez-Seara Alonso, M. Teresa; València Guitart, Marta (1997)
    Article
    Open Access
    The linear oscillator equation with a frequency depending slowly on time is used to test a method to compute exponentially small quantities. This work present the matching method in the complex plane as a tool to obtain ...
  • Exponentially small splitting of separatrices in the perturbed McMillan map 

    Martínez-Seara Alonso, M. Teresa; Martín de la Torre, Pablo; Sauzin, D. (2009-12)
    External research report
    Open Access
    The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. ...
  • Exponentially small splitting of separatrices in the perturbed McMillan map 

    Martín, Pau; Sauzin, D.; Martínez-Seara Alonso, M. Teresa (2011-10)
    Article
    Open Access
    The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic xed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. ...
  • Resurgence in a Hamilton-Jacobi equation 

    Olivé, Carme; Sauzin, D.; Martínez-Seara Alonso, M. Teresa (2002)
    Article
    Open Access
    We study the resurgent structure associated with a Hamilton-Jacobi equation. This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching. ...
  • Resurgence of inner solutions for perturbations of the McMillan map 

    Martínez-Seara Alonso, M. Teresa; Sauzin, D.; Martín de la Torre, Pablo (2009-12)
    External research report
    Open Access
    A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove ...
  • Resurgence of inner solutions for perturbations of the McMillan map 

    Martín, Pau; Sauzin, D.; Martínez-Seara Alonso, M. Teresa (2011-09)
    Article
    Open Access
    Abstract. A sequence of \inner equations" attached to certain perturbations of the McMillan map was considered in [5], their solutions were used in that article to measure an exponentially small separatrix splitting. We ...
  • Two Examples of Resurgence 

    Olivé, Carme; Sauzin, D.; Martínez-Seara Alonso, M. Teresa (2003)
    Article
    Open Access
    This paper gives an account of two articles which illustrate the use of Resurgence theory for estimating the diference between two complex invariant manifolds associated with the area-preserving H?enon map for the first ...