Browsing by Author "Guàrdia Munarriz, Marcel"
Now showing items 120 of 27

A counterexample to the theorem of Laplace–Lagrange on the stability of semimajor axes
Clarke, Andrew Michael; Fejoz, Jacques; Guàrdia Munarriz, Marcel (202404)
Article
Open AccessA 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 finitegap tori for the 2D cubic NLS equation
Guàrdia Munarriz, Marcel; Hani, Zaher; Haus, Emanuele; Maspero, Alberto; Procesi, Michela (20190101)
Article
Restricted access  publisher's policyWe present the recent result in [29] concerning strong nonlinear instability and growth of Sobolev norms near quasiperiodic finitegap solutions of the defocusing cubic nonlinear Schrödinger equation (NLS) on the twodimensional ... 
A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems
Guàrdia Munarriz, Marcel; Kaloshin, Vadim; Zhang, Jianlu (20161101)
Article
Open AccessIn this paper we study a socalled 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 codimension2 sliding bifurcations in the dry friction oscillator
MartínezSeara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Hogan, S. John (2010)
Article
Restricted access  publisher's policyIn this paper, we analytically consider sliding bifurcations of periodic orbits in the dryfriction 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 (20190312)
Article
Open AccessFor 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 Hopfzero singularity: rigorous computation of the stokes constant
Baldomá Barraca, Inmaculada; Capinski, Maciej J.; Guàrdia Munarriz, Marcel; MartínezSeara Alonso, M. Teresa (20230401)
Article
Open AccessConsider analytic generic unfoldings of the three dimensional conservative Hopfzero singularity. Under open conditions on the parameters determining the singularity, the unfolding possesses two saddlefoci 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 (20221029)
Article
Open AccessThe Restricted 3Body 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 (20210721)
Research report
Open AccessThe Restricted 3Body 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 ... 
Chaoticlike transfers of energy in hamiltonian PDEs
Giuliani, Filippo; Guàrdia Munarriz, Marcel; Martín de la Torre, Pablo; Pasquali, Stefano (Springer Nature, 20210101)
Article
Open AccessWe 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 kinkdefect interaction models: rigorous results
MartínezSeara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Gomide, Otávio M.L. (20200101)
Article
Open AccessIn this work we study a model of interaction of kinks of the sineGordon equation with a weak defect. We obtain rigorous results concerning the socalled critical velocity derived in [7] by a geometric approach. More ... 
Exponentially and nonexponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
Guàrdia Munarriz, Marcel; MartínezSeara Alonso, M. Teresa (201107)
Research report
Open AccessIn 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
MartínezSeara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Olivé, Carme (2010)
Article
Restricted access  publisher's policyIn 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; MartínezSeara Alonso, M. Teresa (2011)
Research report
Open AccessIn this paper we study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a nonautonomous perturbation which is fast and periodic in time. We provide ... 
Generic bifurcations of low codimension of planar Filippov Systems
MartínezSeara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Teixeira, Marco Antonio (201102)
Article
Restricted access  publisher's policyIn this article some qualitative and geometric aspects of nonsmooth 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; MartínezSeara Alonso, M. Teresa; Teixeira, Marco Antonio (200910)
Research report
Open AccessIn this article some qualitative and geometric aspects of nonsmooth 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 T2
Guàrdia Munarriz, Marcel; Sandhaus, Evan; Procesi, M. (20161001)
Article
Open AccessWe consider the completely resonant nonlinear 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 (20140316)
Article
Open AccessFix 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 AccessWe 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 threebody problem
Guàrdia Munarriz, Marcel; Kaloshin, Vadim; Fejoz, J.; Roldán González, Pablo (2016)
Article
Open AccessWe study the dynamics of the restricted planar threebody 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; MartínezSeara Alonso, M. Teresa; Zgliczynski, Piotr; Martín de la Torre, Pablo (Elsevier, 20220525)
Article
Open AccessConsider 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 ...