• DOI:10.1512/iumj.2022.71.8969
• Corpus ID: 214611563

On Brolin's theorem over the quaternions

@article{Bisi2020OnBT,
  title={On Brolin's theorem over the quaternions},
  author={Cinzia Bisi and Antonino De Martino},
  journal={Indiana University Mathematics Journal},
  year={2020}
}

• C. Bisi, A. 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 considering both a quaternionic polynomial with real coefficients and a polynomial with coefficients in a slice but not all real. Brolin's theorems for the one slice preserving polynomials and for generic polynomials are also proved.