Continuous time evolution from iterated maps and Carleman linearization
  Using the Carleman linearization technique the continuous iteration of a mapping is studied. Based on the detailed analysis of the Carleman embedding matrix the precise mathematical meaning is given to such notion. The ordinary differential equations referring to continuous iterations are identified and the discussion of the relationship between them and the corresponding iterated maps is performed.   Keywords: iterated systems, functional eigenequation 
P. Gralewicz and K. Kowalski