44 citations · 170 across the 35 of their papers we have counts for
37 papers
Stochastic behavior along mean motion resonances in the restricted planar 3-body problem
Marcel Guardia, Vadim Kaloshin, Pau Martín +1
One of the most remarkable instability zones in the Solar system are Kirkwood gaps in the asteroid belt. In this paper we analyze instabilities in the famous Kirkwood gap in…
Computation of a separatrix map and a normally hyperbolic invariant lamination for the RP3BP
Marcel Guardia, Vadim Kaloshin, Pau Martín +1
In this paper we discuss the existence of a normally hyperbolic invariant lamination (NHIL) at the Kirkwood gap for the Restricted Planar Elliptic 3 Body Problem. This proble…
Second-species dynamics in the restricted planar circular three body problem: chaos, final motions and periodic orbits
Marcel Guardia, José Lamas, Tere M-Seara
Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodi…
Partially hyperbolic dynamics in the 3-body problem
Marcel Guardia, Jaime Paradela
We construct symplectic blenders for two classical Hamiltonian systems: the 3-body problem and its restricted version. We use these objects to show that both models exhibit a robus…
Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
Marcel Guardia, José Lamas, Tere M. Seara
In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the prima…
A remark on the onset of resonance overlap
Jacques Fejoz, Marcel Guardia
Chirikov's celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigourous. We…
A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes
Andrew Clarke, Jacques Fejoz, Marcel Guardia
A longstanding belief has been that the semimajor axes, in the Newtonian planetary problem, are stable. In the course of the XIX century, Laplace, Lagrange and others gave stronger…
Effective chaos for the Kirchhoff equation on tori
Pietro Baldi, Filippo Giuliani, Marcel Guardia +1
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity i…
A degenerate Arnold diffusion mechanism in the Restricted 3 Body Problem
Marcel Guardia, Jaime Paradela, Tere M. Seara
A major question in dynamical systems is to understand the mechanisms driving global instability in the 3 Body Problem (3BP), which models the motion of three bodies under Newtonia…
Why are inner planets not inclined?
Andrew Clarke, Jacques Fejoz, Marcel Guardia
Poincaré's work more than one century ago, or Laskar's numerical simulations from the 1990's on, have irrevocably impaired the long-held belief that the Solar System should be stab…
Hyperbolic dynamics and oscillatory motions in the 3 Body Problem
Marcel Guardia, Pau Martín, Jaime Paradela +1
Consider the planar 3 Body Problem with masses . In this paper we address two fundamental questions: the existence of oscillatory motions and of chaotic hyperbolic s…
Breakdown of heteroclinic connections in the analytic Hopf-Zero singularity: Rigorous computation of the Stokes constant
Inmaculada Baldomá, Maciej J. Capiński, Marcel Guardia +1
Consider analytic generic unfoldings of the three dimensional conservative Hopf-Zero singularity. Under open conditions on the parameters determining the singularity, the unfolding…
Topological Shadowing Methods in Arnold Diffusion: Weak Torsion and Multiple Time Scales
Andrew Clarke, Jacques Fejoz, Marcel Guardia
Consider a symplectic map which possesses a normally hyperbolic invariant manifold of any even dimension with transverse homoclinic channels. We develop a topological shadowing arg…
Arnold diffusion in Hamiltonian systems on infinite lattices
Filippo Giuliani, Marcel Guardia
We consider a system of infinitely many penduli on an -dimensional lattice with a weak coupling. For any prescribed path in the lattice, for suitable couplings, we construct orb…
Sobolev norms explosion for the cubic NLS on irrational tori
Filippo Giuliani, Marcel Guardia
We consider the cubic nonlinear Schrödinger equation on -dimensional irrational tori. We construct solutions which undergo growth of Sobolev norms. More concretely, for every $s…
Breakdown of homoclinic orbits to L3 in the RPC3BP (I). Complex singularities and the inner equation
Inmaculada Baldomá, Mar Giralt, Marcel Guardia
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…
Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula
Inmaculada Baldomá, Mar Giralt, Marcel Guardia
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 p…
On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting
Otávio M. L. Gomide, Marcel Guardia, Tere M. Seara +1
Breathers are nontrivial time-periodic and spatially localized solutions of nonlinear dispersive partial differential equations (PDEs). Families of breathers have been found for ce…
Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem
Maciej J. Capiński, Marcel Guardia, Pau Martín +2
Consider the Restricted Planar Circular 3 Body Problem with both realistic mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence of all possible combinati…
Symbolic Dynamics in the Elliptic Isosceles Restricted Three Body Problem
Marcel Guardia, Jaime Paradela, Tere-M. Seara +1
The elliptic isosceles restricted three body problem (REI3BP) models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodi…
Chaotic Resonant Dynamics and Exchanges of Energy in Hamiltonian PDEs
Filippo Giuliani, Marcel Guardia, Pau Martin +1
The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on the 2-dimensional torus exchanging ener…
Chaotic-like transfers of energy in Hamiltonian PDEs
Filippo Giuliani, Marcel Guardia, Pau Martin +1
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on and we prove the existence of different types of solutions which exchange energy b…
Critical velocity in kink-defect interaction models: rigorous results
Otávio M. L. Gomide, Marcel Guardia, Tere M. Seara
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…
Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
Marcel Guardia, Zaher Hani, Emanuele Haus +2
We consider the defocusing cubic nonlinear Schrödinger equation (NLS) on the two-dimensional torus. The equation admits a special family of elliptic invariant quasiperiodic tori ca…