14 citations · 15 across the 6 of their papers we have counts for
6 papers
Some Symmetric Pyramids with trivial Dehn invariant
Guillaume Duval
For some symmetric pyramids of , we find Galois obstruction for their Dehn invariant to be zero, i.e. for the pyramids to be scissor equivalent to a cube. These conditions ar…
Isochrony in 3D radial potentials. From Michel Hénon ideas to isochrone relativity: classification, interpretation and applications
Alicia Simon-Petit, Jérôme Perez, Guillaume Duval
Revisiting and extending an old idea of Michel Hénon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in pote…
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…