112 citations · 193 across the 13 of their papers we have counts for
9 papers · 1 filter
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…
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…
Globally minimizing parabolic motions in the Newtonian N-body problem
Ezequiel Maderna, Andrea Venturelli
We consider the -body problem in with the newtonian potential . We prove that for every initial configuration and for every minimizing normalized centr…
On weak KAM theory for N-body problems
Ezequiel Maderna
We consider N-body problems with homogeneous potential where , including the Newtonian case (). Given and , we find a uniform upper bound fo…