论文标题
探索热带微分方程
Exploring tropical differential equations
论文作者
论文摘要
本文的目的是四倍。首先是从头开始发展热带差异代数几何形状的理论。第二个是介绍差分代数几何形状的热带基本定理，并展示如何用于在阿基马群岛（复杂分析）和非archimedean（例如，$ p $ $ $ -ADIC）设置中提取有关电源系列解决方案集合的组合信息。第三个子公司的目的是展示热带差异代数几何形状是半自然的应用，而这样做则有助于差异代数几何形状的评估研究。我们使用这种形式主义将部分差分代数的几何形状的基本定理扩展到任意（有限）许多变量的形式电源序列序列的差异分数；为此，我们制作了非krull估值的新例子，值得自己进一步研究。
The purpose of this paper is fourfold. The first is to develop the theory of tropical differential algebraic geometry from scratch; the second is to present the tropical fundamental theorem for differential algebraic geometry, and show how it may be used to extract combinatorial information about the set of power series solutions to a given system of differential equations, both in the archimedean (complex analytic) and in the non-archimedean (e.g., $p$-adic) settings. A third and subsidiary aim is to show how tropical differential algebraic geometry is a natural application of semiring theory, and in so doing, contribute to the valuative study of differential algebraic geometry. We use this formalism to extend the fundamental theorem of partial differential algebraic geometry to the differential fraction field of the ring of formal power series in arbitrarily (finitely) many variables; in doing so we produce new examples of non-Krull valuations that merit further study in their own right.
