INSTABILITIES AND HOMOCLINIC PHENOMENA IN HAMILTONIAN SYSTEMS
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 Download
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 Download
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 Download
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 Download
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 Download
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 Download
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 Download
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 Download
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. Nonlinearity34 4983 (2021). DOI: 10.1088/1361-6544/ac0483 Download
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 Download
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
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. Download
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. Download
F. Giuliani, M. Guardia, Arnold diffusion in Hamiltonian systems on infinite lattices, arXiv:2204.10602v1, preprint April 2022. Download
A. Clarke, J. Fejoz, M. Guardia, Topological Shadowing Methods in Arnold Diffusion: Weak Torsion and Multiple Time Scales, arXiv:2204.14135v1, preprint May 2022. Download
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. Download