  In this paper, we consider a monic, centred, hyperbolic polynomial of degree
$d \ge 2$, restricted on its Julia set and compute its Lyapunov exponents with
respect to certain weighted Lyubich's measures. In particular, we show a
certain well-behavedness of some coefficients of the Lyapunov exponents, that
quantifies the non-well-behavedness in a system.
