Lyapunov exponents of polynomials with respect to certain weighted Lyubich's measures

Abstract

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.