Related papers: Differential Galois Theory and Integration
Given a planar differential system with a first integral, we show how to find a normalizer. For systems with a center, we give an integral formula for the derivative of its period function.
Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable…
We study discretization of Darboux integrable systems. The discretization is done by using $x$- or $y$-integrals of the considered systems. New examples of semi-discrete Darboux integrable systems are obtained.
The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.
In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a…
We study a necessary condition for the integrability of the polynomials fields in the plane by means of the differential Galois theory. More concretely, by means of the variational equations around a particular solution it is obtained a…
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that…
For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, 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…
We prove that algebraic solutions of Garnier systems in the irregular case are of two types. The classical ones come from isomonodromic deformations of linear equations with diagonal or dihedral differential Galois group; we give a complete…
We develop a Galois theory for systems of linear difference equations with periodic parameters, for which we also introduce linear difference algebraic groups. We then apply this to constructively test if solutions of linear q-difference…
An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
We extend Kovacic's algorithm to compute the differential Galois group of some second order parameterized linear differential equation. In the case where no Liouvillian solutions could be found, we give a necessary and sufficient condition…
In this paper we analyze the tangential symmetries of Darboux integrable decomposable exterior differential systems. The decomposable systems generalize the notion of a hyperbolic exterior differential system and include the classic notion…
For a field k$with an automorphism \sigma and a derivation \delta, we introduce the notion of liouvillian solutions of linear difference-differential systems {\sigma(Y) = AY, \delta(Y) = BY} over k and characterize the existence of…
An algorithm to give an explicit description of all the solutions to any tropical linear system $A\odot x=B\odot x$ is presented. The given system is converted into a finite (rather small) number $p$ of pairs $(S,T)$ of classical linear…
The question of how Algebra can be used to solve dynamical systems and characterize chaos was first posed in a fertile mathematical context by Ziglin, Morales, Ramis and Sim\'o using differential Galois theory. Their study was aimed at…
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic…