02/24/2013, 09:13 PM
How many fixpoints does zeta have actually ?
If a fractal converges to a single fixpoint then that is the only fixpoint.
So I guess the question is how many fixpoints does zeta have ?
afterall if x is distinct from y and zeta(x)=x and zeta(y)=y then taking zeta zeta zeta ... zeta(y) = y ( and not x ! ).
attractive or not is another matter.
Notice that zeta(x+yi) for x >> y gives 1 and zeta(...zeta(1)...) = x
I also note that zeta(z) = 1 + 1/2^z + ... so for Re(z) > 1 and abs(z) = oo we get the same limit as for zeta (...zeta (1)...).
regards
tommy1729
If a fractal converges to a single fixpoint then that is the only fixpoint.
So I guess the question is how many fixpoints does zeta have ?
afterall if x is distinct from y and zeta(x)=x and zeta(y)=y then taking zeta zeta zeta ... zeta(y) = y ( and not x ! ).
attractive or not is another matter.
Notice that zeta(x+yi) for x >> y gives 1 and zeta(...zeta(1)...) = x
I also note that zeta(z) = 1 + 1/2^z + ... so for Re(z) > 1 and abs(z) = oo we get the same limit as for zeta (...zeta (1)...).
regards
tommy1729