EN
Let f be a quadratic map (more generally, $f(z) = z^d + c$, d > 1) of the complex plane. We give sufficient conditions for f to have no measurable invariant linefields on its Julia set. We also prove that if the series $∑_{n≥0} 1/(fⁿ)'(c)$ converges absolutely, then its sum is non-zero. In the proof we use analytic tools, such as integral and transfer (Ruelle-type) operators and approximation theorems.