论文标题
在布洛林定理上
On Brolin's theorem over the quaternions
论文作者
论文摘要
在本文中，我们在$ \ mathbb {h} $上调查了布洛林定理，四季节的偏斜场。此外，考虑到具有真实系数的Quaternionic多项式$ p $，我们专注于其平衡度量的特性，以及其他措施的混合属性和Lyapunov指数。我们证明了一个中心极限定理，并根据四离子平衡度量来计算拓扑熵和可测量的熵。我们证明它们是相等的，考虑到具有实际系数的四离子多项式和具有系数的多项式多项式，但并非全部。还证明了Brolin的一个切片保留多项式和通用多项式的定理。
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.
