Gottfried Wrote:bo198214 Wrote:What also burningly interests me how this looks with other functions that have an attractive fixed point.
I think for our example \( f(x)=x^2+x-1/16 \) with fixed points \( \pm 1/4 \) this does no more work, that the eigenvalues of the Carleman matrices converge to the powers of the derivative at one fixed point.
Well, I see, that the sequence of sets of eigenvalues of truncations of increasing size of the Carleman-matrix C is not stabilizing. But we have this with the Bb-matrices as well, if we use b outside 1..e^(1/e) - so I don't think we have really a problem here.
No problem? You mean that the coefficients of the functional exponential or of the \( t \)-th iterate converge despite (with increasing matrix size)?