Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9520041 | Comptes Rendus Mathematique | 2005 | 6 Pages |
Abstract
For a positive integer n and R>0, we set BRn={xâRn|âxââ1 we construct a sequence of analytic perturbations (Hj) of the completely integrable Hamiltonian â(r)=12(r12+â¯+rnâ12)+rn on TnÃBRn, with unstable orbits for which we can estimate the time of drift in the action space. These functions Hj are analytic on a fixed complex neighborhood V of TnÃBRn, and if Éj:=âHjâââC0(V) the time of drift of these orbits is smaller than exp(c(1/Éj)1/2(nâ3)) for a fixed constant c>0. Our unstable orbits pass close to a doubly resonant surface, so the result is almost optimal since the stability exponent for such orbits is 1/2(nâ2). To cite this article: J.-P. Marco, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jean-Pierre Marco,