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math.CA2018
On the convergence of an exotic formal series solution of an ODE
Renat Gontsov, Irina Goryuchkina
A sufficient condition of the convergence of an exotic formal series (a kind of power series with complex exponents) solution to an ODE of a general form is proposed.
math-ph2018
Triangular Schlesinger systems and superelliptic curves
Vladimir Dragović, Renat Gontsov, Vasilisa Shramchenko
We study the Schlesinger system of partial differential equations in the case when the unknown matrices of arbitrary size are triangular and the eigenvalues of each m…
math.CA2018
A note on the convergence of multivariate formal power series solutions of meromorphic Pfaffian systems
Renat Gontsov, Irina Goryuchkina
Here we present some compliments to theorems of Gerard and Sibuya, on the convergence of multivariate formal power series solutions of nonlinear meromorphic Pfaffian systems. Their…