Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Bagayoko, Vincent"'
Autor:
Bagayoko, Vincent
We study conjugacy of formal derivations on fields of generalised power series in characteristic 0. Casting the problem of Poincar\'e resonance in terms of asymptotic differential algebra, we give conditions for conjugacy of parabolic flat log-exp tr
Externí odkaz:
http://arxiv.org/abs/2409.17036
Autor:
Bagayoko, Vincent
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
Externí odkaz:
http://arxiv.org/abs/2409.16251
Autor:
Bagayoko, Vincent
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 in order to solve regular equations over groups using simple valuatio
Externí odkaz:
http://arxiv.org/abs/2409.14854
Autor:
Bagayoko, Vincent
We introduce a formalism for considering infinite, linearly ordered products in groups. Using this, we define infinite compositions in certain groups of formal power series and show that such series can sometimes be represented as infinite, linearly
Externí odkaz:
http://arxiv.org/abs/2403.07368
Autor:
Bagayoko, Vincent, Krapp, Lothar Sebastian, Kuhlmann, Salma, Panazzolo, Daniel, Serra, Michele
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 field $k(\!(G)\!)$ of generalised power series, exploiting our knowledge
Externí odkaz:
http://arxiv.org/abs/2403.05827
Autor:
Bagayoko, Vincent
Log-atomic numbers are surreal numbers whose iterated logarithms are monomials, and consequently have a trivial expansion as transseries. Presenting surreal numbers as sign sequences, we give the sign sequence formula for log-atomic numbers. To that
Externí odkaz:
http://arxiv.org/abs/2402.15800
Autor:
Bagayoko, Vincent Mamoutou
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 as certain groups $\mathcal{G}_{\mathcal{M}}$ of infinitely large germs
Externí odkaz:
http://arxiv.org/abs/2402.00549
Surreal numbers form the ultimate extension of the field of real numbers with infinitely large and small quantities and in particular with all ordinal numbers. Hyperseries can be regarded as the ultimate formal device for representing regular growth
Externí odkaz:
http://arxiv.org/abs/2310.14879
For any ordinal $\alpha > 0$, we show how to define a hyperexponential $E_{\omega^{\alpha}}$ and a hyperlogarithm $L_{\omega^{\alpha}}$ on the class $\mathbf{No}^{>, \succ}$ of positive infinitely large surreal numbers. Such functions are archetypes
Externí odkaz:
http://arxiv.org/abs/2310.14873
Conway's field No of surreal numbers comes both with a natural total order and an additional "simplicity relation" which is also a partial order. Considering No as a doubly ordered structure for these two orderings, an isomorphic copy of No into itse
Externí odkaz:
http://arxiv.org/abs/2305.02001