Publications

PUBLICATIONS

• M. Guardia, Z. Hani, E. Haus, A. Maspero and M. Procesi.  A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation. Rendiconti Lincei – Matematica e Applicazioni. 30 (2019), pp 865–880
  DOI: 10.4171/RLM/873
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• M. Guardia, V. Kaloshin and J. Zhang.  Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis.  233 (2019) Issue 2, pp 799–836.
  DOI: 10.1007/s00205-019-01368-7
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• O.M.L. Gomide, M. Guardia, T-M. Seara. Critical velocity in kink-defect interaction models: Rigorous results. Journal of Differential Equations (2020).
  DOI: 10.1016/j.jde.2020.02.030
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• R. Feola, F. Giuliani, M. Procesi. Reducible KAM Tori for the Degasperis-Procesi equation. Commun. Math. Phys. (2020) 377, 1681–1759.
  DOI: 10.1007/s00220-020-03788-z 
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• F. Giuliani, M. Guardia, P. Martin, S. Pasquali. Chaotic-like Transfers of Energy in Hamiltonian PDEs. Commun. Math. Phys. (2021)
  DOI: 10.1007/s00220-021-03956-9
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• F. Giuliani, M. Guardia, P. Martin, S. Pasquali, Chaotic Resonant Dynamics and Exchanges of Energy in Hamiltonian PDEs, Rendiconti Lincei – Matematica e Applicazioni. 32 (2021), pp 149–165.
  DOI: 10.4171/RLM/931
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• F. Giuliani. Transfers of energy through fast diffusion channels in some resonant PDEs on the circle. Discrete & Continuous Dynamical Systems (2021).
  DOI: 10.3934/dcds.2021068
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• M. Guardia, J. Paradela, T-M. Seara and C. Vidal. Symbolic Dynamics in the restricted elliptic isosceles three body problem. Journal of Differential Equations (2021).
  DOI: 10.1016/j.jde.2021.05.017
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• R. Feola and F. Giuliani, Quasi Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity. Memoirs of the American Mathematical Society (2021). 
• M. Gallone and S. Pasquali, Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction. Nonlinearity 34 4983 (2021).
  DOI: 10.1088/1361-6544/ac0483
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• I. Baldomá, M. Giralt, and M. Guardia, Breakdown of homoclinic orbits to L3 in the RPC3BP — I: Complex singularities and the inner equation.  Advances in Mathematics 408(6):108562  (2022). 
  DOI: 10.1016/j.aim.2022.108562
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• R. Feola, F. Giuliani, Time Quasi-Periodic Traveling Gravity Water Waves in Infinite Depth, Rendiconti Lincei – Matematica e Applicazioni. Vol. 31, No. 4 (2022) pp. 901–916.
  DOI: 10.4171/RLM/919
  
• M. J. Capiński, M. Guardia, P. Martín, T-M. Seara, P. Zgliczyński, Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem, Journal of Differential Equations (2022).
  DOI: 10.1016/j.jde.2022.02.056
• F. Giuliani, M. Guardia, Sobolev norms explosion for the cubic NLS on irrational tori, Nonlinear Analysis (2022) 
  DOI: 10.1016/j.na.2022.112865
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PREPRINTS

• O. M. L. Gomide, M. Guardia, T. M. Seara and C. Zeng, On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting, arXiv:2107.14566, preprint July 2021.
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• I. Baldomá, M. Giralt, and M. Guardia, Breakdown of homoclinic orbits to L3 in the RPC3BP — II: An asymptotic formula, arXiv:2107.09941, preprint July 2021.
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• F. Giuliani, M. Guardia, Arnold diffusion in Hamiltonian systems on infinite lattices, arXiv:2204.10602v1, preprint April 2022. 
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• A. Clarke, J. Fejoz, M. Guardia, Topological Shadowing Methods in Arnold Diffusion: Weak Torsion and Multiple Time Scales, arXiv:2204.14135v1, preprint May 2022. 
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• I. Baldomá, M.J. Capinski, M. Guardia, T.M. Seara, Breakdown of heteroclinic connections in the analytic Hopf-Zero singularity: Rigorous computation of the Stokes constant, arXiv:2206.13840v1, preprint June 2022. 
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