09/10/2010, 12:00 AM

poincare functional equation

F(az) = f(f(z)) with abs(a) > 1 and f(z) holomorphic @ z = 0

F(0) = f(0) = 0 f '(0) = a

always has a solution F(z) holomorhic @ z = 0.

if F ' (0) = 1 we have uniqueness. ( poincare function ).

** !! IF f(z) is entire then so is F(z) !! **

might be usefull to someone.

regards

tommy1729

F(az) = f(f(z)) with abs(a) > 1 and f(z) holomorphic @ z = 0

F(0) = f(0) = 0 f '(0) = a

always has a solution F(z) holomorhic @ z = 0.

if F ' (0) = 1 we have uniqueness. ( poincare function ).

** !! IF f(z) is entire then so is F(z) !! **

might be usefull to someone.

regards

tommy1729