Now showing items 1-20 of 27

    • A counterexample to the theorem of Laplace–Lagrange on the stability of semimajor axes 

      Clarke, Andrew Michael; Fejoz, Jacques; Guàrdia Munarriz, Marcel (2024-04)
      Article
      Open Access
      A longstanding belief has been that the semimajor axes, in the Newtonian planetary problem, are stable. Our the course of the XIX century, Laplace, Lagrange and others gave stronger and stronger arguments in this direction, ...
    • A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation 

      Guàrdia Munarriz, Marcel; Hani, Zaher; Haus, Emanuele; Maspero, Alberto; Procesi, Michela (2019-01-01)
      Article
      Restricted access - publisher's policy
      We present the recent result in [29] concerning strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap solutions of the defocusing cubic nonlinear Schrödinger equation (NLS) on the two-dimensional ...
    • A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems 

      Guàrdia Munarriz, Marcel; Kaloshin, Vadim; Zhang, Jianlu (2016-11-01)
      Article
      Open Access
      In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin ...
    • An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator 

      Martínez-Seara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Hogan, S. John (2010)
      Article
      Restricted access - publisher's policy
      In this paper, we analytically consider sliding bifurcations of periodic orbits in the dry-friction oscillator. The system depends on two parameters: F, which corresponds to the intensity of the friction, and ω, the ...
    • Asymptotic density of collision orbits in the restricted circular planar 3 body problem 

      Guàrdia Munarriz, Marcel; Kaloshin, Vadim; Zhang, Jianlu (2019-03-12)
      Article
      Open Access
      For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(µ120) dense as µ¿0 .
    • Breakdown of heteroclinic connections in the analytic Hopf-zero singularity: rigorous computation of the stokes constant 

      Baldomá Barraca, Inmaculada; Capinski, Maciej J.; Guàrdia Munarriz, Marcel; Martínez-Seara Alonso, M. Teresa (2023-04-01)
      Article
      Open Access
      Consider analytic generic unfoldings of the three- dimensional conservative Hopf-zero singularity. Under open conditions on the parameters determining the singularity, the unfolding possesses two saddle-foci when the ...
    • Breakdown of homoclinic orbits to L3 in the RPC3BP (I). Complex singularities and the inner equation 

      Baldomá Barraca, Inmaculada; Giralt Miron, Mar; Guàrdia Munarriz, Marcel (2022-10-29)
      Article
      Open Access
      The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies, called the primaries. If the primaries perform circular motions and the massless body ...
    • Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula 

      Baldomá Barraca, Inmaculada; Giralt Miron, Mar; Guàrdia Munarriz, Marcel (2021-07-21)
      Research report
      Open Access
      The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that ...
    • Chaotic-like transfers of energy in hamiltonian PDEs 

      Giuliani, Filippo; Guàrdia Munarriz, Marcel; Martín de la Torre, Pablo; Pasquali, Stefano (Springer Nature, 2021-01-01)
      Article
      Open Access
      We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on T2 and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. ...
    • Critical velocity in kink-defect interaction models: rigorous results 

      Martínez-Seara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Gomide, Otávio M.L. (2020-01-01)
      Article
      Open Access
      In this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More ...
    • Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation 

      Guàrdia Munarriz, Marcel; Martínez-Seara Alonso, M. Teresa (2011-07)
      Research report
      Open Access
      In this paper we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian System of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables ...
    • Exponentially small splitting for the pendulum: a classical problem revisited 

      Martínez-Seara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Olivé, Carme (2010)
      Article
      Restricted access - publisher's policy
      In this paper, we study the classical problem of the exponentially small splitting of separatrices of the rapidly forced pendulum. Firstly, we give an asymptotic formula for the distance between the perturbed invariant ...
    • Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results 

      Baldomá Barraca, Inmaculada; Fontich, Ernest; Guàrdia Munarriz, Marcel; Martínez-Seara Alonso, M. Teresa (2011)
      Research report
      Open Access
      In this paper we study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation which is fast and periodic in time. We provide ...
    • Generic bifurcations of low codimension of planar Filippov Systems 

      Martínez-Seara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Teixeira, Marco Antonio (2011-02)
      Article
      Restricted access - publisher's policy
      In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local(and global) bifurcations in ...
    • Generic bifurcations of low codimension of planar Filippov Systems 

      Guàrdia Munarriz, Marcel; Martínez-Seara Alonso, M. Teresa; Teixeira, Marco Antonio (2009-10)
      Research report
      Open Access
      In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local (and global) bifurcations ...
    • Growth of Sobolev norms for the analytic NLS on T-2 

      Guàrdia Munarriz, Marcel; Sandhaus, Evan; Procesi, M. (2016-10-01)
      Article
      Open Access
      We consider the completely resonant non-linear Schrödinger equation on the two dimensional torus with any analytic gauge invariant nonlinearity. Fix s>1. We show the existence of solutions of this equation which achieve ...
    • Growth of sobolev norms for the cubic defocusing NLS with a convolution potential 

      Guàrdia Munarriz, Marcel (2014-03-16)
      Article
      Open Access
      Fix s > 1. Colliander et al. proved in (Invent Math 181:39–113, 2010 )the existence of solutions of the cubic defocusing nonlinear Schrödinger equation in the two torus whose s -Sobolev norm undergoes arbitrarily large ...
    • Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation 

      Guàrdia Munarriz, Marcel; Kaloshin, Vadim (2015)
      Article
      Open Access
      We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix s>1. Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with s -Sobolev norm growing ...
    • Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem 

      Guàrdia Munarriz, Marcel; Kaloshin, Vadim; Fejoz, J.; Roldán González, Pablo (2016)
      Article
      Open Access
      We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem ...
    • Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem 

      Capinski, Maciej J.; Guàrdia Munarriz, Marcel; Martínez-Seara Alonso, M. Teresa; Zgliczynski, Piotr; Martín de la Torre, Pablo (Elsevier, 2022-05-25)
      Article
      Open Access
      Consider the Restricted Planar Circular 3 Body Problem. If the trajectory of the body of zero mass is defined for all time, it can have the following four types of asymptotic motion when time tends to infinity forward or ...