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