For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...

for the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. when the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. in this paper we will consider the polynomial planar vector fields ...

In this paper we study the Fuchsian Riemann-Hilbert (inverse monodromy) problem corresponding to Frobenius structures on Hurwitz spaces. We find a solution to this Riemann-Hilbert problem in terms of integrals of certain meromorphic differentials over a basis of an appropriate relative homology space over a Riemann surface, study the corresponding monodromy group and compute the monodromy matri...

A monodromy transform approach, presented in this communication, provides a general base for solution of space-time symmetry reductions of Einstein equations in all known integrable cases, which include vacuum, electrovacuum, massless Weyl spinor field and stiff fluid, as well as some string theory induced gravity models. There were found a special finite set of functional parameters which are ...

The classical second order Lamé equation contains a so-called accessory parameter B. In this paper we study for which values of B the Lamé equation has a monodromy group which is conjugate to a subgroup of SL(2,R) (unitary monodromy with indefinite hermitian form). We refomulate the problem as a spectral problem and give an asymptotic expansion for the spectrum.

We describe the qualitative features of the joint spectrum of the quantum 1:1:2 resonant swing spring. The monodromy of the classical analogue of this problem is studied in Dullin et al. [Physica D 190, 15–37 (2004)]. Using symmetry arguments and numerical calculations we compute its three-dimensional (3D) lattice of quantum states and show that it possesses a codimension 2 defect characterized...

Here we solve N × N Riemann-Hilbert (inverse monodromy) problems with all monodromy matrices having the structure of matrices of quasi-permutation (i.e. matrices which have only one non-zero element in each column and each row). Such RiemannHilbert problem may be associated to arbitrary Hurwitz space of algebraic curves L of genus g realized as N -sheeted covering over CP1, and allowes solution...