Geodesic
The n-centre problem of celestial mechanics for large energies
Journal of the European Mathematical Society, Tome 4 (2002) no. 1, pp. 1-114

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

We consider the classical three-dimensional motion in a potential which is the sum of n attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the n centres, we find a universal behaviour for all energies E above a positive threshold. Whereas for n=1 there are no bounded orbits, and for n=2 there is just one closed orbit, for nS3 the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of this hyperbolic set. Then we set up scattering theory, including symbolic dynamics of the scattering orbits and differential cross section estimates. The theory includes the n-centre problem of celestial mechanics, and prepares for a geometric understanding of a class of restricted n-body problems. To allow for applications in semiclassical molecular scattering, we include an additional smooth (electronic) potential which is arbitrary except its Coulombic decay at infinity. Up to a (optimal) relative error of order 1/E, all estimates are independent of that potential but only depend on the relative positions and strengths of the centres. Finally we show that different, non-universal, phenomena occur for collinear configurations.
DOI : 10.1007/s100970100037
Classification : 58-XX, 70-XX, 00-XX
Keywords: 
@article{JEMS_2002_4_1_a0,
     author = {Andreas Knauf},
     title = {The n-centre problem of celestial mechanics for large energies},
     journal = {Journal of the European Mathematical Society},
     pages = {1--114},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {2002},
     doi = {10.1007/s100970100037},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970100037/}
}
TY  - JOUR
AU  - Andreas Knauf
TI  - The n-centre problem of celestial mechanics for large energies
JO  - Journal of the European Mathematical Society
PY  - 2002
SP  - 1
EP  - 114
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s100970100037/
DO  - 10.1007/s100970100037
ID  - JEMS_2002_4_1_a0
ER  - 
%0 Journal Article
%A Andreas Knauf
%T The n-centre problem of celestial mechanics for large energies
%J Journal of the European Mathematical Society
%D 2002
%P 1-114
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s100970100037/
%R 10.1007/s100970100037
%F JEMS_2002_4_1_a0
Andreas Knauf. The n-centre problem of celestial mechanics for large energies. Journal of the European Mathematical Society, Tome 4 (2002) no. 1, pp. 1-114. doi: 10.1007/s100970100037

Cité par Sources :