The paper computes the Brouwer degree of some classes of homogeneous polynomials defined on quaternions and applies the results, together with a continuation theorem of coincidence degree theory, to the existence and multiplicity of periodic solutions of a class of systems of quaternionic valued ordinary differential equations. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

中文翻译：

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度数、四元数和周期解

论文计算了定义在四元数上的若干类齐次多项式的 Brouwer 度，并将结果与​​重合度理论的延拓定理一起应用于一类四元数常微分方程组周期解的存在性和多重性。本文是主题问题“微分方程和差分方程中的拓扑度和不动点理论”的一部分。