3 citations · 11 across the 19 of their papers we have counts for
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McGehee blowup for Lagrangian systems and instability of equilibria
J. M. Burgos
We prove that total instability is a generic phenomenon in the real analytic class of electromagnetic Lagrangian systems under a weak magnetism hypothesis. The main object in the p…
On the Lagrange-Dirichlet converse in dimension three
Juan M. Burgos, Miguel Paternain
Consider a mechanical system with a real analytic potential. We prove that in dimension three, there is an open and dense subset of the set of non strict local minimums of the pote…
A proof of the Palamodov's total instability conjecture
J. M. Burgos
We give for the first time a detailed proof of the Palamodov's total instability conjecture in Lagrangian dynamics. This proves an older related Lyapunov instability conjecture pos…
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…
Existence of partially hyperbolic motions in the N-body problem
Juan Manuel Burgos
In the context of the Newtonian N-body problem, we prove the existence of a partially hyperbolic motion with prescribed positive energy and any initial collisionless configuration.…
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…