Controlling chaos

1. Elementary Celestial and Hamiltonian Mechanics 2. Quasi-Integrable Hamiltonian System 3. Kam Tori 4. Single Resonance Dyanmics 5. Numerical Tools for the Detection of Chaos 6. Interactions Among Resonances 7. Secular Dynamics of the Planets 8. Secular Dynamics of Small Bodies 9. Mean Motion Resonances 10. Three Body Resonances 11. Secular Dynamics Inside Mean Motion Resonances 12. Global Dynamical Structure of the Belts of Small Bodies.

Modern celestial mechanics : aspects of solar system dynamics

Nekhoroshev estimates for quasi-convex hamiltonian systems

Hamiltonian long-wave approximations to the water-wave problem

We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/σ)], σ being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.

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Superexponential stability of KAM tori

CONTENTSChapter I. IntroductionChapter II. Stability in the neighbourhood of a periodic torusChapter III. Stability for arbitrary initial conditionsChapter IV. Transpositions, applications, prospects §1. Additional variables and an application to celestial mechanics §2. Transposition to other contexts and degenerate cases §3. Systems with (infinitely) many degrees of freedom §4. Steepness, quasi-convexity, and closed orbitsChapter V. Robust tori; Arnol'd diffusion §1. Robust tori and "normalization" §2. Arnol'd diffusionAppendix 1. Some Diophantine approximationAppendix 2. Gevrey asymptotic expansionsReferences

P Lochak

Papers

Canonical perturbation theory via simultaneous approximation