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Hyperseries subfields of surreal numbers
Vincent Bagayoko
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 hyperser…
Formal conjugacy and asymptotic differential algebra
Vincent Bagayoko
We study conjugacy of formal derivations on fields of generalised power series in characteristic 0. Casting the problem of Poincaré resonance in terms of asymptotic differential al…
Equations over valued groups
Vincent Bagayoko
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings…
Groups with infinite linearly ordered products
Vincent Bagayoko
We introduce a formalism of infinite, linearly ordered products in general groups. Using this, we define infinite compositions in certain groups of formal power series such as tran…
Automorphisms and derivations on algebras endowed with formal infinite sums
Vincent Bagayoko, Lothar Sebastian Krapp, Salma Kuhlmann +2
We establish a correspondence between automorphisms and derivations on certain algebras of generalised power series. In particular, we describe a Lie algebra of derivations on a fi…
Sign sequences of log-atomic numbers
Vincent Bagayoko
Log-atomic numbers are surreal numbers whose iterated logarithms are monomials, and consequently have a trivial expansion as transseries. Presenting surreal numbers as sign sequenc…
On ordered groups of regular growth rates
Vincent Mamoutou Bagayoko
We introduce an elementary class of linearly ordered groups, called growth order groups, encompassing certain groups under composition of formal series (e.g. transseries) as well a…