Related papers: Global integrability of cosmological scalar fields
We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as introduced by Morales-Ruiz and Ramis. The…
This is the second part of integrability analysis of cosmological models with scalar fields. Here, we study systems with conformal coupling, and show that apart from four cases, where explicit first integrals are known, the generic system…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
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…
In this paper we present a short material concerning to some results in Morales-Ramis theory, which relates two different notions of integrability: Integrability of Hamiltonian Systems through Liouville Arnold Theorem and Integrability of…
This is an example of application of Ziglin-Morales-Ramis algebraic studies in Hamiltonian integrability, more specifically the result by Morales, Ramis and Sim\'o on higher-order variational equations, to the well-known…
Relativistic Hamiltonian equations describing a motion of a point mass in an arbitrary homogeneous potential are considered. For the first time, the necessary integrability conditions for integrability in the Liouville sense for this class…
In this paper we study the general concept of integrability in the broad sense within the frame of differential Galois theory. We concentrate on the gradient systems which are not integrable. In spite of it, if we consider them as the real…
This paper is an overview of our works which are related to investigations of the integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations with homogeneous velocity independent forces. The two types of…
We derive necessary conditions for integrability in the Liouville sense of natural Hamiltonian systems with homogeneous potential of degree zero. We derive these conditions through an analysis of the differential Galois group of variational…
The basic theory of Differential Galois and in particular Morales--Ramis theory is reviewed with focus in analyzing the non--integrability of various problems of few bodies in Celestial Mechanics. The main theoretical tools are:…
For finite dimensional Hamiltonian systems derived from 1+1 dimensional integrable systems, if they have Lax representations, then the Lax operator creates a set of conserved integrals. When these conserved integrals are in involution, it…
We consider a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background space with an ideal gas and a multifield Lagrangian consisting of two minimally coupled scalar fields which evolve in a field space of constant curvature.…
We study the integrable model with minimally and non-minimally coupled scalar fields and the correspondence of their general solutions. Using the model with a minimally coupled scalar field and a the constant potential as an example we…
We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the…
We consider the problem of $n$ points with positive masses interacting pairwise with forces inversely proportional to the distance between them. In particular, it is the classical gravitational, Coulomb or photo-gravitational $n$-body…
We generalise Langlois' Hamiltonian treatment of gauge-invariant linear cosmological perturbations to a cosmological setting with multiple scalar fields minimally coupled to gravity. We review the Hamilton-Jacobi-like technique for a…
We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous…
In this paper we are studying the meromorphic integrability of a two-dimensional Hamiltonian system with a homogeneous potential of degree 6. The approach used in this work is the theory of the Ziglin-Moralez-Ruiz-Ramis-Simo. Within the…
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this problem is equivalent to that of solvability of the Lie algebra…