Lyapunov Characteristic Exponents are Nonnegative
Lyapunov Characteristic Exponents are Nonnegative
We prove that, for an arbitrary rational map $f$ on the Riemann sphere and an arbitrary probability invariant measure on the Julia set, Lyapunov characteristic exponents are nonnegative a.e. In particular $\log |fâ|$ is integrable. An analogous theorem is proved for smooth maps of an interval with all critical points …