05/28/2014, 12:23 PM

Let f(z) be an analytic function with a riemann surface that has branches.

Let RB be shorthand for going from one specific Riemann Branch to another specific one.

Then the equation that holds locally or globally :

RB ( f(z) ) = f( p(z) )

with p(z) a degree 1 or 2 polynomial.

fascinates me.

For instance f(2z+1) is another branch of f(z).

That is fascinating.

But how to solve such a thing ?

in particular

RB ( f(z) ) = f(z + C)

This relates to tetration and dynamics.

Not sure if its in the books.

Btw do not confuse with a simple invariant :

p (f(z)) is another branch of f(z).

which is different !!

regards

tommy1729

Let RB be shorthand for going from one specific Riemann Branch to another specific one.

Then the equation that holds locally or globally :

RB ( f(z) ) = f( p(z) )

with p(z) a degree 1 or 2 polynomial.

fascinates me.

For instance f(2z+1) is another branch of f(z).

That is fascinating.

But how to solve such a thing ?

in particular

RB ( f(z) ) = f(z + C)

This relates to tetration and dynamics.

Not sure if its in the books.

Btw do not confuse with a simple invariant :

p (f(z)) is another branch of f(z).

which is different !!

regards

tommy1729