Theorem KAM
The theorem KAM is a theorem of traditional Mécanique in its Hamiltonian formulation. It owes its name with initial of three mathematicians: Kolmogorov, Arnold and Moser. Conjectured by Kolmogorov in 1954, it was rigorously shown some time after and separately by Arnold and Moser, these two authors using of the assumptions of regularity on the Hamiltonien a little different.
The importance of this theorem comes owing to the fact that it was thought formerly that the ergodic Hypothèse of Boltzmann applied to all the not-integrable dynamic systems. A first setting at fault of this assumption was obtained in 1953 with the result of the Expérience of Fermi-Pasta-Ulam. Theorem KAM teaches us in a rigorous way that the disturbance of a integrable Système necessarily did not lead to a system ergodic, but that tori invariants could remain in areas of finished measurements of the space of the phases, corresponding to small islands where the dynamics of the disturbed system remains quasi-periodical.
Related articles
- Experiment of Fermi-Pasta-Ulam
- ergodic Theory
- Theory of chaos
- Celestial mechanics
- Jürgen K. Moser | Andrei Kolmogorov | Vladimir Arnold
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