6 citations · 13 across the 16 of their papers we have counts for
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Turrittin's Theorem revisited. The real case
Moulay Barkatou, Félix Álvaro Carnicero-Martín, Fernando Sanz Sánchez
We establish a real version of Turrittin's result on polynomial and formal normal forms of linear systems of ODEs with meromorphic coefficients. Both the normal forms or the transf…
Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory
Primitivo Acosta-Humánez, Moulay Barkatou, Raquel Sánchez-Cauce +1
Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprising…
Linear Differential Systems with Small Coefficients: Various Types of Solvability and their Verification
Moulay A. Barkatou, Renat R. Gontsov
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this pro…
Formal Solutions of Singularly Peturbed Linear Differential Systems
Moulay A. Barkatou, Suzy S. Maddah
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computatio…
On the Reduction of Singularly-Perturbed Linear Differential Systems
Moulay Barkatou, Suzy S. Maddah, Hassan Abbas
In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal intege…
Apparent Singularities of Linear Difference Equations with Polynomial Coefficients
S. A. Abramov, M. A. Barkatou, M. van Hoeij
Let L be a linear difference operator with polynomial coefficients. We consider singularities of L that correspond to roots of the trailing (resp. leading) coefficient of L. We pro…