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arXiv · 2304.06791

An algebraic structure of groups of solutions of the third Aczel-Jabotinsky formal differential equation

Wojciech Jablonski·Ludwig Reich
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Abstract

We study the algebraic structure of the groups of solutions of the third Acz{\'e}l-Jabotinsky differential equation $(H\circ \Phi)(x)=\frac{d\Phi}{d x}\cdot H(x)$ in the rings of formal power series and truncated formal power series $k[[x]]_s$, where $s$ is either a positive integer or $s=\infty$ and $H\in k[[x]]_s$ is given. We give also the detailed description of all solutions of this equation.

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Wojciech Jablonski, Ludwig Reich. 2023-04-13. An algebraic structure of groups of solutions of the third Aczel-Jabotinsky formal differential equation. https://arxiv.org/abs/2304.06791

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