On Brolin's theorem over the quaternions

  title={On Brolin's theorem over the quaternions},
  author={Cinzia Bisi and Antonino De Martino},
  journal={Indiana University Mathematics Journal},
  • C. BisiA. Martino
  • Published 22 March 2020
  • Mathematics
  • Indiana University Mathematics Journal
In this paper we investigate the Brolin's theorem over $\mathbb{H}$, the skew field of quaternions. Moreover, considering a quaternionic polynomial $p$ with real coefficients, we focus on the properties of its equilibrium measure, among the others, the mixing property and the Lyapunov exponents of the measure. We prove a central limit theorem and we compute the topological entropy and measurable entropy with respect to the quaternionic equilibrium measure. We prove that they are equal… 
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