Generation theory on the unit disk

For physical, chemical, and biological applications it is sometimes preferable to study a great variety of iterative processes, including the processes of continuous time. In spite of their simplicity these processes have been applicable in many fields, involving mathematical areas such as geometry, theory of stochastic branching processes, operator theory on Hardy spaces, and optimizations methods. A problem that has interested mathematicians since the time of Abel is how to define n-th iterate of function when n is not integer.