112 citations · 193 across the 13 of their papers we have counts for
14 papers
A natural decomposition of the Jacobi equation for some classes of -body problems
Renato Iturriaga, Ezequiel Maderna
We consider several -body problems. The main result is a very simple and natural criterion for decoupling the Jacobi equation for some classes of them. If is a Euclidean spa…
Uniqueness of hyperbolic Busemann functions in the Newtonian N-body problem
Ezequiel Maderna, Andrea Venturelli
For the N-body problem we prove that any two hyperbolic rays having the same limit shape define the same Busemann function. We localize a region of differentiability for these func…
On the Lyapunov instability in Lagrangian dynamics
J. M. Burgos, M. Paternain
In the context of mechanical Lagrangian dynamics, we prove a new Lyapunov instability criterion for a non strict local minimum equilibrium point of a smooth potential where the suf…
Geodesic rays of the -body problem
Juan Manuel Burgos, Ezequiel Maderna
For the Newtonian N-body problem, we study the Jacobi-Maupertuis metric of the nonnegative energy levels. We show that the geodesic rays are expansive, that is to say, all the dist…
Viscosity solutions and hyperbolic motions: a new PDE method for the -body problem
Ezequiel Maderna, Andrea Venturelli
We prove for the -body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level of th…
On the Lyapunov instability in Newtonian dynamics
Juan Manuel Burgos, Ezequiel Maderna, Miguel Paternain
We prove Lyapunov instability for cases in which the local minimum of the potential energy is reached on a hypersurface of the configuration space. In contrast to the known results…