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HamInstab SIGNED

Instabilities and homoclinic phenomena in Hamiltonian systems

Total Cost €

0

EC-Contrib. €

0

Partnership

0

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 HamInstab project word cloud

Explore the words cloud of the HamInstab project. It provides you a very rough idea of what is the project "HamInstab" about.

gravitational    physically    diffusion    ouml    gordon    scarce    resonances    secular    deeply    hyperbolic    theory    manifolds    solutions    instability    connections    dimensional    differential    plan    push    pdes    phenomena    leads    arnold    mean    instabilities    setting    oscillatory    global    arbitrarily    proper    mechanics    localized    model    nevertheless    mathematical    dynamics    intersection    energy    existence    interaction    wave    infinite    hamiltonian    transfer    integrable    relying    puntual    motion    perturbation    periodic    dinger    usually    stability    nonlinear    drifting    time    construct    body    techniques    framework    averages    prove    partial    solution    objects    heteroclinic    analyze    astronomers    effect    masses    invariant    breathers    dynamical    orbits    homoclinic    accumulates    klein    motions    modes    schr    showing    equations    transversal    nearly    fundamental    models    force    stationary    ascertain    celestial    place   

Project "HamInstab" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITAT POLITECNICA DE CATALUNYA 

Organization address
address: CALLE JORDI GIRONA 31
city: BARCELONA
postcode: 8034
website: www.upc.edu

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Spain [ES]
 Project website https://haminstab.barcelonatech-upc.eu/
 Total cost 1˙100˙347 €
 EC max contribution 1˙100˙347 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-STG
 Funding Scheme ERC-STG
 Starting year 2018
 Duration (year-month-day) from 2018-01-01   to  2022-12-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAT POLITECNICA DE CATALUNYA ES (BARCELONA) coordinator 1˙100˙347.00

Map

 Project objective

A fundamental problem in the study of dynamical systems is to ascertain whether the effect of a perturbation on an integrable Hamiltonian system accumulates over time and leads to a large effect (instability) or it averages out (stability). Instabilities in nearly integrable systems, usually called Arnold diffusion, take place along resonances and by means of a framework of partially hyperbolic invariant objects and their homoclinic and heteroclinic connections.

The goal of this project is to develop new techniques, relying on the role of invariant manifolds in the global dynamics, to prove the existence of physically relevant instabilities and homoclinic phenomena in several problems in celestial mechanics and Hamiltonian Partial Differential Equations.

The N body problem models the interaction of N puntual masses under gravitational force. Astronomers have deeply analyzed the role of resonances in this model. Nevertheless, mathematical results showing instabilities along them are rather scarce. I plan to develop a new theory to analyze the transversal intersection between invariant manifolds along mean motion and secular resonances to prove the existence of Arnold diffusion. I will also apply this theory to construct oscillatory motions.

Several Partial Differential Equations such as the nonlinear Schrödinger, the Klein-Gordon and the wave equations can be seen as infinite dimensional Hamiltonian systems. Using dynamical systems techniques and understanding the role of invariant manifolds in these Hamiltonian PDEs, I will study two type of solutions: transfer of energy solutions, namely solutions that push energy to arbitrarily high modes as time evolves by drifting along resonances; and breathers, spatially localized and periodic in time solutions, which in a proper setting can be seen as homoclinic orbits to a stationary solution.

 Publications

year authors and title journal last update
List of publications.
2019 Marcel Guardia, Vadim Kaloshin, Jianlu Zhang
Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem
published pages: 799-836, ISSN: 0003-9527, DOI: 10.1007/s00205-019-01368-7
Archive for Rational Mechanics and Analysis 233/2 2019-08-05

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