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

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

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 6, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.13140/rg.2.2.29599.38560