Research

Selected publications

• Otávio M. L. Gomide, Marcel Guardia, Tere M. Seara, Chongchun Zeng
  On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting
  Inventiones Mathematicae, published online (2025). Available at arXiv.
• Andrew Clarke, Jacques Fejoz, Marcel Guardia
  Why are inner planets not inclined?
  Publications mathématiques de l’IHÉS, published online (2024). Available at arXiv.
  Quanta Magazine: ‘New Proof Finds the ‘Ultimate Instability’ in a Solar System Model‘.
• Marcel Guardia, Filippo Giuliani
  Arnold diffusion in Hamiltonian systems on infinite lattices
  Comm. Pure Appl. Math. 77 (2024), no. 8, 3333–3426. Available at arXiv.
• Marcel Guardia, Zaher Hani, Emanuele Haus, Alberto Maspero, Michela Procesi
  Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
  J. Eur. Math. Soc. (JEMS) 25 (2023), no. 4, 1497–1551. Available at arXiv.
• Jacques Féjoz, Marcel Guardia, Vadim Kaloshin, Pablo Roldan
  Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
  Journal of the European Mathematical Society, 18(10): 2315-2403 (2016). See the preprint version on the arXiv.
• Marcel Guardia, Pau Martin, Tere M. Seara
  Oscillatory motions for the restricted planar circular three body problem
  Inventiones Mathematicae, 203(2): 417-492 (2016). See the preprint version on the arXiv.
• Marcel Guardia, Vadim Kaloshin
  Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
  Journal of the European Mathematical Society, 17 (1): 71–149 (2015). [PDF].

Preprints

• Inmaculada Baldomá, Marcel Guardia, Dmitry E. Pelinovsky
  On a countable sequence of homoclinic orbits arising near a saddle-center point
  Available at arXiv.
• Inmaculada Baldomá, Mar Giralt, Marcel Guardia
  Coorbital homoclinic and chaotic dynamics in the Restricted 3-Body Problem
  Available at arXiv.
• Marcel Guardia, Jaime Paradela, Tere M. Seara
  A degenerate Arnold diffusion mechanism in the Restricted 3 Body Problem
  Available at arXiv.
• Marcel Guardia, Pau Martín, Jaime Paradela, Tere M. Seara
  Hyperbolic dynamics and oscillatory motions in the 3 Body Problem
  Available at arXiv.

Full list of publications

• Marcel Guardia, José Lamas, Tere M. Seara
  Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
  To appear in Communications in Mathematical Physics. Available at arXiv.
• Elisa Maria Alessi, Inmaculada Baldomá, Mar Giralt, Marcel Guardia, Alexandre Pousse
  On the role of the fast oscillations in the secular dynamics of the lunar coplanar perturbation on Galileo satellites
  To appear in Communications in Nonlinear Science and Numerical Simulation. Available at arXiv.
• Elisa Maria Alessi, Inmaculada Baldomá, Mar Giralt, Marcel Guardia
  On the Arnold diffusion mechanism in Medium Earth Orbit
  To appear in Journal of Nonlinear Science. Available at arXiv.
• Otávio M. L. Gomide, Marcel Guardia, Tere M. Seara, Chongchun Zeng
  On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting
  Inventiones Mathematicae, published online (2025). Available at arXiv.
• Andrew Clarke, Jacques Fejoz, Marcel Guardia
  Why are inner planets not inclined?
  Publications mathématiques de l’IHÉS, published online (2024). Available at arXiv.
• Inmaculada Baldomá, Maciej J. Capiński, Mar Giralt, Marcel Guardia
  Breakdown of homoclinic orbits to L3: Nonvanishing of the Stokes constant
  To appear in Discrete and Continuous Dynamical Systems A. Available at arXiv.
• Pietro Baldi, Filippo Giuliani, Marcel Guardia, Emanuele Haus
  Effective chaos for the Kirchhoff equation on tori
  To appear in Annales de l’Institut Henri Poincaré C. Available at arXiv.
• Marcel Guardia, Filippo Giuliani
  Arnold diffusion in Hamiltonian systems on infinite lattices
  Comm. Pure Appl. Math. 77 (2024), no. 8, 3333–3426. Available at arXiv.
• Clarke, Andrew; Fejoz, Jacques; Guardia, Marcel
  A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes
  Arch. Ration. Mech. Anal. 248 (2024), no. 2, Paper No. 19, 73 pp.
• Fejoz, Jacques; Guardia, Marcel
  A remark on the onset of resonance overlap
  Regul. Chaotic Dyn. 28 (2023), no. 4-5, 578–584.
• Baldomá, Inmaculada; Giralt, Mar; Guardia, Marcel
  Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula
  Adv. Math. 430 (2023), Paper No. 109218, 72 pp.
• Marcel Guardia, Zaher Hani, Emanuele Haus, Alberto Maspero, Michela Procesi
  Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
  J. Eur. Math. Soc. (JEMS) 25 (2023), no. 4, 1497–1551. Available at arXiv.
• Baldomá, Inmaculada; Capiński, Maciej J.; Guardia, Marcel; Seara, Tere M.
  Breakdown of heteroclinic connections in the analytic Hopf-zero singularity: rigorous computation of the Stokes constant
  J. Nonlinear Sci. 33 (2023), no. 2, Paper No. 28, 47 pp.
• Clarke, Andrew; Fejoz, Jacques; Guàrdia, Marcel
  Topological shadowing methods in Arnold diffusion: weak torsion and multiple time scales
  Nonlinearity 36 (2023), no. 1, 426–457.
• Baldomá, Inmaculada; Giralt, Mar; Guardia, Marcel
  Breakdown of homoclinic orbits to L3 in the RPC3BP (I). Complex singularities and the inner equation
  Adv. Math. 408 (2022), Paper No. 108562, 64 pp.
• Giuliani, Filippo; Guardia, Marcel
  Sobolev norms explosion for the cubic NLS on irrational tori
  Nonlinear Anal. 220 (2022), Paper No. 112865, 25 pp.
• Capiński, Maciej J.; Guardia, Marcel; Martín, Pau; M-Seara, Tere; Zgliczyński, Piotr
  Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem
  J. Differential Equations 320 (2022), 316–370.
• Guardia, Marcel; Paradela, Jaime; Seara, Tere M.; Vidal, Claudio
  Symbolic dynamics in the restricted elliptic isosceles three body problem
  J. Differential Equations 294 (2021), 143–177.
• Giuliani, Filippo; Guardia, Marcel; Martin, Pau; Pasquali, Stefano
  Chaotic-like transfers of energy in Hamiltonian PDEs
  Comm. Math. Phys. 384 (2021), no. 2, 1227–1290.
• Giuliani, Filippo; Guardia, Marcel; Martin, Pau; Pasquali, Stefano
  Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs
  Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 32 (2021), no. 1, 149–166.
• Gomide, Otávio M. L.; Guardia, Marcel; Seara, Tere M.
  Critical velocity in kink-defect interaction models: rigorous results
  J. Differential Equations 269 (2020), no. 4, 3282–3346.
• Marcel Guardia, Zaher Hani, Emanuele Haus, Alberto Maspero, Michela Procesi
  A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
  Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), no. 4, 865–880. Available on arXiv.
• Marcel Guardia, Vadim Kaloshin, Jianlu Zhang
  Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem
  Archive for Rational Mechanics and Analysis, 233(2): 799-836 (2019). See the preprint version on arXiv.
• Marcel Guardia, Pau Martin, Lara Sabbagh, Tere M. Seara
  Oscillatory orbits in the restricted elliptic planar three body problem
  Discrete and Continuous Dynamical Systems A, 37(1): 229-256 (2017). See the preprint version on arXiv.
• Emanuele Haus, Marcel Guardia, Michela Procesi
  Growth of Sobolev norms for the analytic NLS on T2
  Advances in Mathematics, 301(1): 615-692 (2016). See the preprint version on the arXiv.
• Marcel Guardia, Vadim Kaloshin, Jianlu Zhang
  A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems
  Communications in Mathematical Physics, 348(1): 321-361 (2016). See the preprint version on the arXiv.
• Jacques Féjoz, Marcel Guardia, Vadim Kaloshin, Pablo Roldan
  Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
  Journal of the European Mathematical Society, 18(10): 2315-2403 (2016). See the preprint version on the arXiv.
• Marcel Guardia, Jacques Féjoz
  Secular instability in the spatial three-body problem
  Archive for Rational Mechanics and Analysis, 221(1): 335-362 (2016). See the preprint version on arXiv.
• Marcel Guardia, Pau Martin, Tere M. Seara
  Oscillatory motions for the restricted planar circular three body problem
  Inventiones Mathematicae, 203(2): 417-492 (2016). See the preprint version on the arXiv.
• Marcel Guardia, Vadim Kaloshin
  Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
  Journal of the European Mathematical Society, 17 (1): 71–149 (2015). [PDF].
• Marcel Guardia
  Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation with a convolution potential
  Communications in Mathematical Physics, 329 (1): 405–434 (2014). [PDF].
• Marcel Guardia
  Splitting of separatrices in the resonances of nearly integrable Hamiltonian Systems of one and a half degrees of freedom
  Discrete and Continuous Dynamical Systems A, 33 (7): 2829-2859 (2013). [PDF].
• Inma Baldomá, Marcel Guardia, Ernest Fontich, Tere M. Seara
  Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results
  Journal of Differential Equations, 253 (12): 3304-3439 (2012). [PDF].
• Marcel Guardia, Tere M. Seara
  Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
  Nonlinearity, 24 (5): 1367-1412 (2012). [PDF].
• Marcel Guardia, Tere M. Seara, Marco Antonio Teixeria
  Generic bifurcations of low codimension of planar Filippov Systems
  Journal of Differential Equations, 250 (4): 1967-2023 (2011) . [PDF].
• Marcel Guardia, S. John Hogan, Tere M. Seara
  An analytical approach to codimension 2 sliding bifurcations in the dry friction oscillator
  SIAM Journal on Applied Dynamical Systems, 9: 769–798 (2010). [PDF].
• Marcel Guardia, Carme Olivé, Tere M. Seara
  Exponentially small splitting for the pendulum: a classical problem revisited
  Journal of Nonlinear Science, 20: 595-685, (2010) . [PDF].

Teaching

This year I am teaching

• Equacions diferencials at the Grau de Matemàtiques.
• Qualitative theory of ODE’s and Hamiltonian systems at the Master in Advanced Mathematics.