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math.DS2020★ 3 cited
A Theorem on Ellipses, an Integrable System and a Theorem of Boltzmann
Giovanni Gallavotti, Ian Jauslin
We study a mechanical system that was considered by Boltzmann in 1868 in the context of the derivation of the canonical and microcanonical ensembles. This system was introduced as…
math.DS2018★ 1 cited
Quasi periodic Hamiltonian Motions, Scale Invariance, Harmonic Oscillators
Giovanni Gallavotti
The work of Kolmogorov, Arnold and Moser appeared just before the renormalization group approach to statistical mechanics was proposed by Wilson: it can be classified as a multisca…
math.DS2004
Degenerate elliptic resonances
Guido Gentile Giovanni Gallavotti
Quasi-periodic motions on invariant tori of an integrable system of dimension smaller than half the phase space dimension may continue to exists after small perturbations. The para…