In the introduction of his book Noncommutative Geometry, p. 42, Connes explains that when a classical dynamical system has enough constants of motions, the motion of the system is almost periodic, and the algebra of observables is the algebra of almost periodic series

$$q(t) = \sum q_{n_1 \dots n_k} \, \exp( 2 \pi i \left\langle n, \nu \right\rangle t),$$

where $n_i$ are integers and $\nu_i$ "fundamental frequencies" (and $\left\langle n, \nu \right\rangle = \sum n_i \nu_i$).

From what does this come from?

I believe that "enough constants of motion" means that the system is somehow integrable, and perhaps the Arnold-Liouville theorem can help provide an answer to this question, but I am not familiar with this domain, and I hope someone will know better what Cones means.


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