On the existence of canonical gyrokinetic variables for chaotic magnetic fields

The gyrokinetic description of particle dynamics faces a basic difficulty when a special type of canonical variables is sought, i.e., the so-called $\mathit{\text{gyrokinetic}}\mathit{\text{canonical}}\mathit{\text{variables}}$. These are defined in such a way that two of them are respectively identified with the gyrophase-angle, describing the fast particle gyration motion around magnetic field lines, and its canonically conjugate momentum. In this paper we intend to discuss the conditions of existence for these variables.