Abstract
In the present paper, we shall study the stability of a near integrable Hamil-tonian system over finite but very long intervals of times. So we look at the system governed by the Hamiltonian:
where (p, q) are action-angle variables of the integrable Hamiltonian h. We assume that H is analytic over some domain G × T n (G ⊂ R n a “nice” domain say convex open) and that h is a convex function ( ∇ 2 h(p) is a sign definite symmetric matrix). The perturbation f is of size ε (see below).
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References
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© 1994 Springer Basel AG
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Lochak, P., Neistadt, A.I., Niederman, L. (1994). Stability of Nearly Integrable Convex Hamiltonian Systems Over Exponentially Long Times. In: Kuksin, S., Lazutkin, V., Pöschel, J. (eds) Seminar on Dynamical Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 12. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7515-8_2
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DOI: https://doi.org/10.1007/978-3-0348-7515-8_2
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