Instabilities and homoclinic phenomena in Hamiltonian systems

Project Information

HamInstab

Grant agreement ID: 757802

DOI 10.3030/757802

Project closed

EC signature date 7 November 2017

Start date 1 January 2018

End date 31 December 2023

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 100 347,50

EU contribution € 1 100 347,50

Coordinated by

UNIVERSITAT DE BARCELONA
Spain

Publications

Peer reviewed articles (22)

Time quasi-periodic traveling gravity water waves in infinite depth

Author(s): Roberto Feola; Filippo Giuliani
Published in: Rendiconti Lincei - Matematica e Applicazioni, Issue 11206330, 2022, ISSN 1120-6330
Publisher: Accademia Nazionale dei Lincei
DOI: 10.4171/rlm/919

Symbolic Dynamics in the Elliptic Isosceles Restricted Three Body Problem

Author(s): Guardia, Marcel; Paradela, Jaime; Seara, Tere-M.; Vidal, Claudio
Published in: Journal of Differential Equations, Issue 2, 2021, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2021.05.017

Breakdown of Heteroclinic Connections in the Analytic Hopf-Zero Singularity: Rigorous Computation of the Stokes Constant

Author(s): Inmaculada Baldomá; Maciej J. Capiński; Marcel Guardia; Tere M. Seara
Published in: Journal of Nonlinear Science, Issue 7, 2023, ISSN 0938-8974
Publisher: Springer Verlag
DOI: 10.1007/s00332-022-09882-x

Sobolev norms explosion for the cubic NLS on irrational tori

Author(s): Filippo Giuliani; Marcel Guardia
Published in: Nonlinear Analysis, Issue 5, 2022, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2022.112865

Arnold diffusion in multidimensional convex billiards

Author(s): Andrew Clark; Dmitry Turaev
Published in: Duke Mathematical Journal, 2023, ISSN 0012-7094
Publisher: Duke University Press
DOI: 10.1215/00127094-2022-0073

Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction

Author(s): Matteo Gallone; Stefano Pasquali
Published in: Nonlinearity, Issue 2, 2021, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ac0483

Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation

Author(s): Marcel Guardia; Zaher Hani; Emanuele Haus; Alberto Maspero; Michela Procesi
Published in: JEMS, Issue 13, 2023, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1200

Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula

Author(s): Inmaculada Baldomá; Mar Giralt; Marcel Guardia
Published in: Advances in Mathematics, Issue 8, 2023, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2023.109218

Generic properties of geodesic flows on analytic hypersurfaces of Euclidean space

Author(s): Clarke, Andrew Michael
Published in: Discrete and Continuous Dynamical Systems, Issue 15, 2022, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2022127

Topological shadowing methods in arnold diffusion: weak torsion and multiple time scales

Author(s): Andrew Clarke; Jacques Fejoz; Marcel Guàrdia
Published in: Nonlinearity, Issue 9, 2022, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/aca5df

Breakdown of homoclinic orbits to L3 in the RPC3BP (I). Complex singularities and the inner equation

Author(s): Baldomá, Inmaculada; Giralt, Mar; Guardia, Marcel
Published in: Advances in Mathematics, Issue 3, 2022, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108562

Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs

Author(s): Filippo Giuliani; Marcel Guardia; Pau Martín; Stefano Pasquali
Published in: Rendiconti Lincei – Matematica e Applicazioni., Issue 3, 2021, ISSN 1120-6330
Publisher: Accademia Nazionale dei Lincei
DOI: 10.4171/rlm/931

Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity

Author(s): Feola, Roberto; Giuliani, Filippo
Published in: Memoirs of the American Mathematical Society, Issue 11, 2021, ISSN 0065-9266
Publisher: American Mathematical Society
DOI: 10.13140/rg.2.2.35018.39368

Effective chaos for the Kirchhoff equation on tori

Author(s): Baldi, Pietro; Giuliani, Filippo; Guardia, Marcel; Haus, Emanuele
Published in: Annales de l'Institut Henri Poincaré C, Issue 5, 2024, Page(s) 1-50, ISSN 0294-1449
Publisher: Elsevier BV
DOI: 10.4171/aihpc/110

Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem

Author(s): Marcel Guardia, Vadim Kaloshin, Jianlu Zhang
Published in: Archive for Rational Mechanics and Analysis, Issue 233/2, 2019, Page(s) 799-836, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-019-01368-7

Critical velocity in kink-defect interaction models: Rigorous results

Author(s): Otávio M.L. Gomide, Marcel Guardia, Tere M. Seara
Published in: Journal of Differential Equations, Issue 269/4, 2020, Page(s) 3282-3346, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2020.02.030

A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation

Author(s): Marcel Guardia, Zaher Hani, Emanuele Haus, Alberto Maspero, Michela Procesi
Published in: Rendiconti Lincei - Matematica e Applicazioni, Issue 30/4, 2019, Page(s) 865-880, ISSN 1120-6330
Publisher: Accademia Nazionale dei Lincei
DOI: 10.4171/RLM/873

Reducible KAM Tori for the Degasperis–Procesi Equation

Author(s): Roberto Feola, Filippo Giuliani, Michela Procesi
Published in: Communications in Mathematical Physics, Issue 377/3, 2020, Page(s) 1681-1759, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-020-03788-z

A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes

Author(s): Fejoz, Jacques; Clarke, Andrew, Michael; Guardia, Marcel
Published in: Archive for Rational Mechanics and Analysis, Issue 1, 2024, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-024-01960-6

Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem

Author(s): Maciej J. Capiński; Marcel Guardia; Pau Martín; Tere M-Seara; Piotr Zgliczyński
Published in: Journal of Differential Equations, Issue 2, 2022, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2022.02.056

Arnold diffusion in Hamiltonian systems on infinite lattices

Author(s): Giuliani, Filippo; Guardia, Marcel
Published in: Communications in Pure and Applied Mathematics, Issue 4, 2024, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.48550/arxiv.2204.10602

Transfers of energy through fast diffusion channels in some resonant PDEs on the circle

Author(s): Filippo Giuliani
Published in: American Institut of Mathematical Science, Issue 7, 2021, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2021068

Non-peer reviewed articles (1)

Chaotic-Like Transfers of Energy in Hamiltonian PDEs

Author(s): Filippo Giuliani; Marcel Guardia; Pau Martín; Stefano Pasquali
Published in: Communications in Mathematical Physics, Issue 00103616, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.13140/rg.2.2.29599.38560