Výsledky vyhledávání - "Marcel Guardia"

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Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem

Autor: Kaloshin, Marcel Guardia Vadim, Zhang, Jianlu

For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set $\mathcal U$ in phase space independent of fixed measure, where the set of initial points which lead to collision is $O(\mu^\frac{1}{20})$ dense as $\mu\rightarr

Externí odkaz: http://arxiv.org/abs/1805.00800

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Breakdown of heteroclinic connections in the analytic Hopf-zero singularity: rigorous computation of the stokes constant

Autor: Inmaculada Baldomá, Maciej J. Capiński, Marcel Guardia, Tere M. Seara

Consider analytic generic unfoldings of the three dimensional conservative Hopf-Zero singularity. Under open conditions on the parameters determining the singularity, the unfolding possesses two saddle-foci when the unfolding parameter is small enoug

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::22e34105e431909222df2fe7975264b7
https://hdl.handle.net/2117/388331

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Symbolic dynamics in the restricted elliptic isosceles three body problem

Autor: Jaime Paradela, Marcel Guardia, Tere M. Seara, Claudio Vidal

Publikováno v: Journal of Differential Equations. 294:143-177

The restricted elliptic isosceles three body problem (REI3BP) models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. The primaries of masses m1 = m2 move along a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f2247f6d61f2f9a2da9edbdf964fb41a
https://doi.org/10.1016/j.jde.2021.05.017

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Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs

Autor: Stefano Pasquali, Pau Martín, Marcel Guardia, Filippo Giuliani

Publikováno v: Rendiconti Lincei - Matematica e Applicazioni. 32:149-166

The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on the 2-dimensional torus exchanging energy among Fourier modes in a \emph{chaotic-like} way. We say that a tra

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::695e5dd52ff86cd942142c9f13f58306
https://doi.org/10.4171/rlm/931

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Sobolev norms explosion for the cubic NLS on irrational tori

Autor: Filippo Giuliani, Marcel Guardia

Publikováno v: Nonlinear Analysis. 220:112865

We consider the cubic nonlinear Schr��dinger equation on $2$-dimensional irrational tori. We construct solutions which undergo growth of Sobolev norms. More concretely, for every $s>0$, $s\neq 1$ and almost every choice of spatial periods we cons

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9d4be00e89e5eb3abb3f90738f03484d
https://doi.org/10.1016/j.na.2022.112865

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

Autor: Inmaculada Baldomá, Mar Giralt, Marcel Guardia

The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies, called the primaries. If the primaries perform circular motions and the massless body is coplanar with them, one has

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b89d6a637546372a06b2616b5af4c79

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Chaotic-like transfers of energy in hamiltonian PDEs

Autor: Filippo Giuliani, Stefano Pasquali, Marcel Guardia, Pau Martín

Publikováno v: Communications in Mathematical Physics
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on T2 and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be conside

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1351839967fd9eb1a2f971bb8778ead6
https://hdl.handle.net/2117/363923

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Growth of Sobolev norms for the analytic NLS onT2

Autor: Emanuele Haus, Michela Procesi, Marcel Guardia

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

We consider the completely resonant non-linear Schrödinger equation on the two dimensional torus with any analytic gauge invariant nonlinearity. Fix s>1. We show the existence of solutions of this equation which achieve arbitrarily large growth of H

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb009dbfe0f74e705820f1544e33ae97
https://doi.org/10.1016/j.aim.2016.06.018

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Growth of Sobolev Norms in the Cubic Nonlinear Schrödinger Equation with a Convolution Potential

Autor: Marcel Guardia

Publikováno v: Communications in Mathematical Physics. 329:405-434

Fix s > 1. Colliander et al. proved in (Invent Math 181:39–113, 2010) the existence of solutions of the cubic defocusing nonlinear Schrodinger equation in the two torus whose s-Sobolev norm undergoes arbitrarily large growth as time evolves. In thi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::5b7d395633deefe0454c42841358d55f
https://doi.org/10.1007/s00220-014-1977-1

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