# 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}
}```
• 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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## References

SHOWING 1-10 OF 44 REFERENCES

• Mathematics
• 2020
We prove a Runge theorem for and describe the homology of axially symmetric open subsets of H.
• Mathematics
Proceedings of the American Mathematical Society, Series B
• 2020
<p>The classical theorem of Picard states that a non-constant holomorphic function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f
Abstract In this paper the existence of a unique measure of maximal entropy for rational endomorphisms of the Riemann sphere is established. The equidistribution of pre-images and periodic points