Canonical transformation in a three-dimensional phase space endowed with
Nambu bracket is discussed in a general framework. Definition of the canonical
transformations is constructed as based on canonoid transformations. It is
shown that generating functions, transformed Hamilton functions and the
transformation itself for given generating functions can be determined by
solving Pfaffian differential equations corresponding to that quantities. Types
of the generating functions are introduced and all of them is listed.
Infinitesimal canonical transformations are also discussed. Finally, we show
that decomposition of canonical transformations is also possible in
three-dimensional phase space as in the usual two-dimensional one.Comment: 19 pages, 1 table, no figures. Accepted for publication in Int. J.
Mod. Phys.
