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Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques

Jean-Pierre Marco — 1996

Annales de l'I.H.P. Physique théorique

Stability and instability for Gevrey quasi-convex near-integrable hamiltonian systems

Jean-Pierre Marco; David Sauzin — 2003

Publications Mathématiques de l'IHÉS

Diffusion times and stability exponents for nearly integrable analytic systems

Pierre Lochak; Jean-Pierre Marco — 2005

Open Mathematics

For a positive integer n and R>0, we set $B_{R}^{n} = \{x \in ℝ^{n} | {∥x∥}_{\infty} < R\}$ . Given R>1 and n≥4 we construct a sequence of analytic perturbations (H j) of the completely integrable Hamiltonian $h (r) = \frac{1}{2} r_{1}^{2} + . . . \frac{1}{2} r_{n - 1}^{2} + r_{n}$ on $𝕋^{n} \times B_{R}^{n}$ , with unstable orbits for which we can estimate the time of drift in the action space. These functions H j are analytic on a fixed complex neighborhood V of $𝕋^{n} \times B_{R}^{n}$ , and setting $ε_{j} : = {∥h - H_{j}∥}_{C^{0} (V)}$ the time of drift of these orbits is smaller than (C(1/ɛ j)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly resonant surface,...

Sur la construction des solutions de seconde espèce dans le problème plan restreint des trois corps

Jean-Pierre Marco; Laurent Niederman — 1995

Annales de l'I.H.P. Physique théorique

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Currently displaying 1 – 4 of 4

Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques

Stability and instability for Gevrey quasi-convex near-integrable hamiltonian systems

Diffusion times and stability exponents for nearly integrable analytic systems

Sur la construction des solutions de seconde espèce dans le problème plan restreint des trois corps