Rigidity of Lyapunov exponents for polynomials

Zhuchao Ji, Junyi Xie, Geng-Rui Zhang

Let $f,g\in \overline{\mathbb{Q}}[z]$ be polynomials of degree $d\ge 2$ with disconnected Julia sets. We prove that they have the same Lyapunov exponent $\mathcal{L}_f=\mathcal{L}_g…