what have we learned on growth cycles analysis?

Business cycles and growth are considered as independent fields for decades. Indeed, after the Second World War, when macroeconomics began to develop through an increased use of mathematical models, the problem of analyzing growth-cycles dynamics appeared as a real (and certainly also mathematical) challenge. Some economists accepted that dichotomy, concentrating their attention on specific questions which they considered as better addressed in models specifically built in order to capture either long-run or short-run issues. Two subfields appeared: on the one side were business cycle theories which focused on understanding detrended data movements; on the other side was long-run growth theory which analyzed the existence and the stability of stationary paths