05/30/2008, 06:08 AM

Thanks, Gottfried,

I tried to summarize my understanding:

If a Taylor series of a function f is a result of diagnolization of some infinite 2D matrix M and it has a matrix inverse M^-1 in the domain (or sub) of function f then continuous iterates of f can be calculated by using these matrixes.

Would that mean that e.g. for a function whose iterates are 2D (like complex t=u+iv=t(u,v)) or generally n arguments, similar operation can be done via 3D and n+1 D matrixes? Or in this case one diagonal can not represent a function?

Ivars

I tried to summarize my understanding:

If a Taylor series of a function f is a result of diagnolization of some infinite 2D matrix M and it has a matrix inverse M^-1 in the domain (or sub) of function f then continuous iterates of f can be calculated by using these matrixes.

Would that mean that e.g. for a function whose iterates are 2D (like complex t=u+iv=t(u,v)) or generally n arguments, similar operation can be done via 3D and n+1 D matrixes? Or in this case one diagonal can not represent a function?

Ivars