Related papers: A Note on a Differential Galois Approach to Path I…

We present a detailed and simplified version of Hrushovski's algorithm that determines the Galois group of a linear differential equation. There are three major ingredients in this algorithm. The first is to look for a degree bound for…

We study a Sturm-Liouville type eigenvalue problem for second-order differential equations on the infinite interval. Here the eigenfunctions are nonzero solutions exponentially decaying at infinity. We prove that at any discrete eigenvalue…

If we consider a q-analogue of linear differential equation, Galoois group of the q-analogue difference equation is still a linear algebraic group. Namely, by a quantization of linear differential equation, Galois group is not quantized. We…

Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…

Let $f:X\to Y$ be a finite ramified Galois covering of algebraic varieties defined over the complex numbers. In this paper, we prove some structure theorems for such coverings in the case that the non-abelian Galois group of the cover is…

We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…

In this work we study the integrability of a family of nonlinear oscillators. Dynamical systems from this family appear in different applications from mechanics to chemistry. We propose an approach for finding first integrals and…

The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…

This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…

This paper introduces a novel approach to understanding Galois theory, one of the foundational areas of algebra, through the lens of machine learning. By analyzing polynomial equations with machine learning techniques, we aim to streamline…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

We establish some comparison results among the different parameterized Galois theories for $q$-difference equations, completing the work by CHatzidakis, Hardouin and Singer, that addresses the problem in the case without parameters. Our…

We study the integrability of a two-dimensional Hamiltonian system with a gyroscopic term and a non-homogeneous potential composed of two homogeneous components of different degrees. The model describes the motion of a particle in a plane…

Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…

In this paper, we develop a theory of Galois descent for equivariant line bundles on partial flag schemes. In particular, we study computational aspects of the classification of descent data of equivariant line bundles attached to…

The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the…

We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation.…

This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…

Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…

By considering a generalisation of the CPM construction, we develop an infinite hierarchy of probabilistic theories, exhibiting compositional decoherence structures which generalise the traditional quantum-to-classical transition.…