  In the article the class of slice regular functions is shown to be closed
under a new regular composition. The new regular composition turns out to be
globally defined in contrast to the locally defined version by Vlacci. Its
advantage over Vlacci's is demonstrated by its associated theory of composition
operators and dynamical systems for slice regular functions. Especially, the
corresponding Littlewood subordination principle and the Denjoy-Wolff type
theorem can be established.
