Additional parameters in inverse monodromy problems

Some addition to the generalized Riemann-Hilbert problem

“…In the case of irreducible representations an expression for the smallest possible number of apparent singular points has been obtained by A. Bolibrukh [5]. Estimates for this number in the case of an arbitrary monodromy were presented in [11], as well as similar estimates in the case of non-Fuchsian singularities.…”

“…, a n and generalized monodromy data. In the construction there necessary arise apparent singularities (at which coefficients of an equation are singular, but solutions are meromorphic, so that a monodromy is trivial), the number of which was estimated in [11]. We present these results in the language of the GRH-problem for systems, although Section 4 is independent of the previous sections.…”

“…. , a n , which was considered in [11]. It was shown there that the Poincaré rank of unique non-Fuchsian (regular) singularity from Plemelj's theorem can be reduced to a value that is not greater than (p − 1)(n − 1).…”

“…It was shown there that the Poincaré rank of unique non-Fuchsian (regular) singularity from Plemelj's theorem can be reduced to a value that is not greater than (p − 1)(n − 1). Section 4 is devoted to the GRH-problem for scalar equations, for which we recall and reformulate results already proved in [11]. The problem is to construct a scalar linear differential equation…”

Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations

“…The definition of the minimal Fuchsian weight of a representation [45] is similar to that for the maximal Fuchsian weight. For any representation χ of the kind (12), for the corresponding bundle E(Λ), and for its decomposition (15) the non-negative integer γ min (χ) = min…”