Related papers: Monodromy approach to the scaling limits in the is…
The isomonodromy deformation equation for a 2x2 matrix linear ODE with a large parameter can be locally reduced to a (hyper)elliptic equation. To globalize this result, we apply the isomonodromy deformation method and obtain the modulation…
In this paper, we study the isomonodromy deformation equations for the $n\times n$ system of first order meromorphic linear ordinary differential equations with two second order poles. We analyze the asymptotic behaviour of the solutions at…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
We study a generalization of the isomonodromic deformation to the case of connections with irregular singularities. We call this generalization Isostokes Deformation. A new deformation parameter arises: one can deform the formal normal…
We study perturbations of linear differential equations, deriving explicit series solutions, using Dyson-type expansions. We analyze the monodromy of deformed solutions in a number of examples, and relate this to cocycles in a cohomological…
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…
We introduce and study isomonodromy transformations of the matrix linear difference equation Y(z+1)=A(z)Y(z) with polynomial (or rational) A(z). Our main result is a construction of an isomonodromy action of Z^{m(n+1)-1} on the space of…
The non-holonomic deformations of non-local integrable systems belonging to the Nonlinear Schrodinger family are studied using the Bi-Hamiltonian formalism as well as the Lax pair method. The non-local equations are first obtained by…
A class of random recursive sequences (Y_n) with slowly varying variances as arising for parameters of random trees or recursive algorithms leads after normalizations to degenerate limit equations of the form X\stackrel{L}{=}X. For…
We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…
We consider a linear $2\times2$ matrix ODE with two coalescing regular singularities. This coalescence is restricted with an isomonodromy condition with respect to the distance between the merging singularities in a way consistent with the…
Galois/monodromy groups attached to parametric systems of polynomial equations provide a method for detecting the existence of symmetries in solution sets. Beyond the question of existence, one would like to compute formulas for these…
In this paper, we investigate the possibility of constructing isomonodromic deformations of logarithmic connections on curves by using ramified covers. We give new examples and prove a classification result.
In this paper, we classify the algebraic isomonodromic deformations that can be obtained through restriction to generic lines of logarithmic flat connections on the complex projective plane $\mathbb{P}^2_\mathbb{C}$ whose singular locus is…
Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant to a good approximation. There are two main ways to trace out isomorphs, the configurational-adiabat method and the…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…
We study the scaling of adsorption isotherms of polyacrylic dispersants on generic surfaces of metallic oxides $XnOm$ as a function of the number of monomeric units, using Electrostatic Dissipative Particle Dynamics simulations. The…
We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…
We combine the newly discovered technique, which computes explicit formulas for the image of an algebraic curve under rational transformation, with techniques that enable to compute braid monodromies of such curves. We use this combination…