Geodesic
Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
Journal of the European Mathematical Society, Tome 18 (2016) no. 10, pp. 2315-2403

Voir la notice de l'article provenant de la source EMS Press

We study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to model Sun–Jupiter–asteroid systems. For the primaries (Sun and Jupiter), we pick a realistic mass ratio μ=10−3 and a small eccentricity e0​>0. The main result is a construction of a variety of non local diffusing orbits which show a drastic change of the osculating (instant) eccentricity of the asteroid, while the osculating semi major axis is kept almost constant. The proof relies on the careful analysis of the circular problem, which has a hyperbolic structure, but for which diffusion is prevented by KAM tori. In the proof we verify certain non-degeneracy conditions numerically.
DOI : 10.4171/jems/642
Classification : 70-XX, 37-XX
Keywords: Three-body problem, instability, resonance, hyperbolicity, Mather mechanism, Arnol’d diffusion, Solar System, Asteroid Belt, Kirkwood gap 
@article{JEMS_2016_18_10_a2,
     author = {Jacques F\'ejoz and Marcel Guardia and Vadim Kaloshin and Pablo Rold\'an},
     title = {Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem},
     journal = {Journal of the European Mathematical Society},
     pages = {2315--2403},
     publisher = {mathdoc},
     volume = {18},
     number = {10},
     year = {2016},
     doi = {10.4171/jems/642},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/642/}
}
TY  - JOUR
AU  - Jacques Féjoz
AU  - Marcel Guardia
AU  - Vadim Kaloshin
AU  - Pablo Roldán
TI  - Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
JO  - Journal of the European Mathematical Society
PY  - 2016
SP  - 2315
EP  - 2403
VL  - 18
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/642/
DO  - 10.4171/jems/642
ID  - JEMS_2016_18_10_a2
ER  - 
%0 Journal Article
%A Jacques Féjoz
%A Marcel Guardia
%A Vadim Kaloshin
%A Pablo Roldán
%T Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
%J Journal of the European Mathematical Society
%D 2016
%P 2315-2403
%V 18
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/642/
%R 10.4171/jems/642
%F JEMS_2016_18_10_a2
Jacques Féjoz; Marcel Guardia; Vadim Kaloshin; Pablo Roldán. Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem. Journal of the European Mathematical Society, Tome 18 (2016) no. 10, pp. 2315-2403. doi: 10.4171/jems/642

Cité par Sources :