in involution
Two functions $f_1$ and $f_2$ are said to be in involution if their Poisson bracket is zero, i.e. ${f_1, f_2} = 0$1.
1
Arnold, V. I. (1989). Mathematical Methods of Classical Mechanics. In Graduate Texts in Mathematics. Springer New York. https://doi.org/10.1007/978-1-4757-2063-1 arnold1989 Mathematical Methods for Classical Mechanics