05/13/2009, 04:52 PM

i was thinking about tetration and came up with important questions.

for the 3rd time !!

are there meromorphic functions f(x) so that they commute with exp(x) ?

thus :

exp(f(x)) = f(exp(x))

related 2nd question :

t ( t(x) ) = exp(x) ( any real analytic t(x) )

g(x) a meromorphic function

t(x) = inverse_g( 1-fixpoint-regular-half-iterate[ exp(g(x)) ] )

related 3rd question :

q(x) a meromorphic function

t ( t(x) ) = exp(x) ( any real analytic t(x) )

1-fixpoint-regular-half-iterate[ exp(q(x)) ] = t( q(x) )

thanks in advance

regards

tommy1729

for the 3rd time !!

are there meromorphic functions f(x) so that they commute with exp(x) ?

thus :

exp(f(x)) = f(exp(x))

related 2nd question :

t ( t(x) ) = exp(x) ( any real analytic t(x) )

g(x) a meromorphic function

t(x) = inverse_g( 1-fixpoint-regular-half-iterate[ exp(g(x)) ] )

related 3rd question :

q(x) a meromorphic function

t ( t(x) ) = exp(x) ( any real analytic t(x) )

1-fixpoint-regular-half-iterate[ exp(q(x)) ] = t( q(x) )

thanks in advance

regards

tommy1729