Monotonicity and a Taylor approximation theorem for transseries
Logic
2026-05-12 v2 Dynamical Systems
Abstract
We show that the composition of omega-series by surreal numbers, or more generally by elements of any confluent field of transseries, is monotonic in its second argument. In particular, omega-series and LE-series interpreted as functions have the intermediate value property. We also deduce a Taylor approximation theorem for omega-series with maximal radius of validity.
Keywords
Cite
@article{arxiv.2601.07747,
title = {Monotonicity and a Taylor approximation theorem for transseries},
author = {Vincenzo Mantova},
journal= {arXiv preprint arXiv:2601.07747},
year = {2026}
}
Comments
15 pages; relaxed assumptions in Theorems A, C and Corollary B; new Corollaries 4.4, 5.4, 5.6 and Remark 5.5; numerous fixes and editorial improvements