Lochak, it combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians.
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This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori. Instability of dynamical systems with many degrees of freedom , Dokl.
Mathematical aspects of classical and celestial mechanics , Springer-Verlag, Berlin, Encyclopaedia of Mathematical Sciences , Tome 3 [Dynamical systems. Khukhro MR Zbl Differential Equations , Tome no. Systems , Tome 24 no. A criterion of steepness for analytic functions , Uspekhi Mat. Nauk , Tome 41 no.
Pure Math. Tome 69 , pp. Canonical perturbation theory: an approach based on joint approximations , Uspekhi Mat.
Nauk , Tome 47 no. Dumas MR Zbl Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian , Chaos , Tome 2 no. Stability of nearly integrable convex Hamiltonian systems over exponentially long times , Seminar on Dynamical Systems St.
Nonlinear Differential Equations Appl.
Tome 12 , pp. The separation of motions in systems with rapidly rotating phase , Prikl. Add co-authors Co-authors. Upload PDF.
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