86 citations · 1k across the 58 of their papers we have counts for
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Integrability of potentials of degree . Second order variational equations between Kolchin solvability and Abelianity
Guillaume Duval, Andrzej J. Maciejewski
In our previous paper: Integrability of Homogeneous potentials of degree . An application of higher order variational equations, we tried to extract some particular stru…
Integrability of Hamiltonian systems with homogeneous potentials of degrees . An application of higher order variational equations
Guillaume Duval, Andrzej J. Maciejewski
The present work is the first of a serie of two papers, in which we analyse the higher variational equations associated to natural Hamiltonian systems, in their attempt to give Gal…
Integrability of natural Hamiltonian systems with homogeneous potentials of degree zero
Guy Casale, Guillaume Duval, Andrzej J. Maciejewski +1
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…
Jordan obstruction to the integrability of Hamiltonian systems with homogeneous potentials
Guillaume Duval, Andrzej J. Maciejewski
In this paper, we consider the natural complex Hamiltonian systems with homogeneous potential , $q\in\C^n$, of degree . The known results of Morales and Ramis g…
Darboux Polynomials and First Integrals of Natural Polynomial Hamiltonian Systems
Andrzej J. Maciejewski, Maria Przybylska
We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an add…
Differential Galois Approach to the Non-integrability of the Heavy Top Problem
Andrzej J. Maciejewski, Maria Przybylska
We study integrability of the Euler-Poisson equations describing the motion of a rigid body with one fixed point in a constant gravity field. Using the Morales-Ramis theory and too…