I don't know if this is the right place to post this, but my question is: if i have an Hamiltonian defined on the whole phase space and a function f which is also defined on the whole phase space and doesn't depend explicitly on time, i know that if its poisson bracket with the Hamiltonian vanishes everywhere, f is a constant of the motion. But what happens if this poisson bracket doesn't vanish everywhere, but only on a subset of the phase space? This subset could be for example the one i get from the equation {f,H}=0(adsbygoogle = window.adsbygoogle || []).push({});

Thanks!

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# Local constants of motion?

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