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
Download - A. Clarke. Generic properties of geodesic flows on analytic hypersurfaces of Euclidean space. Discrete and Continuous Dynamical Systems, 2022, 42(12): 5839-5868.
DOI: 10.3934/dcds.2022127 - A. Clarke, J. Fejoz, M. Guardia, Topological Shadowing Methods in Arnold Diffusion: Weak Torsion and Multiple Time Scales, Nonlinearity 36 426 (2023).
DOI: 10.1088/1361-6544/aca5df
Download - I. Baldomá, M.J. Capiński, M. Guardia, T-M. Seara, Breakdown of Heteroclinic Connections in the Analytic Hopf-Zero Singularity: Rigorous Computation of the Stokes Constant. Journal of Nonlinear Science, 33, 28 (2023)
DOI: 10.1007/s00332-022-09882-x
Download - M. Guardia, Z. Hani, E. Haus, A. Maspero, M. 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.
DOI: 10.4171/JEMS/1200
Download - A. Clarke, D. Turaev, Arnold diffusion in multidimensional convex billiards. Duke Math. J. 172(10) 1813 – 1878, 15 July 2023.
DOI: 10.1215/00127094-2022-0073 - I. Baldomá, M. Giralt, M. Guardia, Breakdown of homoclinic orbits to L3 in the RPC3BP — II: An asymptotic formula, Advances in Mathematics, Volume 430, 1 October 2023, 109218
DOI: 10.1016/j.aim.2023.109218 - F. Giuliani, M. Guardia, Arnold diffusion in Hamiltonian systems on infinite lattices, Wiley Online Publications, 21 November 2023
DOI: 10.1002/cpa.22191 / arXiv:2204.10602v1 - P. Baldi, F. Giuliani, M. Guardia, E. Haus, Effective chaos for the Kirchhoff equation on tori. Ann. Inst. H. Poincaré Anal. Non Linéaire, pp. 1–50, 1 February 2024.
DOI: 10.4171/AIHPC/110 / arXiv:2303.00688 - A. Clarke, J. Fejoz, M. Guardia, A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes. Archive for Rational Mechanics and Analysis. February 2024.
DOI: 10.1007/s00205-024-01960-6
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.
- M. Guardia, P. Martín, J. Paradela, T. M. Seara, Hyperbolic dynamics and oscillatory motions in the 3 Body Problem. arXiv:2207.14351
- A. Clarke, J. Fejoz, M. Guardia, Why are inner planets not inclined?. arXiv:2210.11311, preprint October 2022.
- J. Paradela, S. Terracini, Oscillatory Motions in the Restricted 3-body Problem: A functional analytic approach. arXiv:2212.05684, preprint December 2022.
- M. Guardia, J. Paradela, T.M. Seara. A degenerate Arnold diffusion mechanism in the Restricted 3 Body Problem. arXiv:2302.06973, preprint February 2023.
- A. Clarke, Geodesics With Unbounded Speed on Fluctuating Surfaces. arXiv:2304.13566, preprint April 2023.
- I. Baldomá, M. J. Capiński, M. Giralt, M. Guardia, Breakdown of homoclinic orbits to L3: Nonvanishing of the Stokes constant. arXiv:2312.13138, preprint December 2023.
- I. Baldomá, M. Giralt, M. Guardia, Coorbital homoclinic and chaotic dynamics in the Restricted 3-Body Problem. arXiv:2312.13819 preprint December 2023.