Abstract
This question is interesting in its own right. It is also related to a more general one in the context of dynamical systems in particular, to a phenomenon called intermittency that occurs in many physical situations. Experimental systems in which it has been observed include ring lasers, fluid layers undergoing convection, chemical reactions and nonlinear electronic circuits, to name a few. In fluid dynamics, the transition from the regular flow of a liquid to turbulent flow under certain conditions is believed to be related to the 'intermittency route to chaos'. What could be the connection between such seemingly unrelated things like the iteration of a hmction and the onset of turbulence? This is surely worth studying in a little more detail.
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