Hyperseries subfields of surreal numbers
Vincent Bagayoko

TL;DR
This paper investigates hyperseries subfields of surreal numbers, establishing methods to define embeddings that preserve complex operations like transfinite sums and hyperfunctions, advancing the understanding of surreal number structures.
Contribution
It introduces a framework for hyperseries fields of surreal numbers with compatible derivations and composition laws, including embedding techniques that preserve advanced operations.
Findings
Defined embeddings that commute with transfinite sums
Established compatibility with hyperexponential and hyperlogarithmic functions
Enhanced the structural understanding of hyperseries subfields
Abstract
We study subfields of surreal numbers, called hyperseries fields, that are suited to be equipped with derivations and composition laws. We show how to define embeddings on hyperseries fields that commute with transfinite sums and all hyperexponential and hyperlogarithmic functions.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems
