Near a fixed point of cos(x) use the method of Schr"oder (1871) ...
http://en.wikipedia.org/wiki/Schr%C3%B6der%27s_equation

Best historical reference: Daniel S. Alexander, A History of Complex Dynamics from Schr"oder to Fatou and Julia (1994).

Near a fixed point of $\cos(x)$ use the method of Schröder (1871) ...
http://en.wikipedia.org/wiki/Schr%C3%B6der%27s_equation

Best historical reference: Daniel S. Alexander, A History of Complex Dynamics from Schröder to Fatou and Julia (1994).