Slice regular composition operators

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.