2 citations · 4 across the 6 of their papers we have counts for
8 papers
Loops, Holonomy and Signature
Juan Alonso, Juan Manuel Burgos, Miguel Paternain
We show that there is a topology on certain groups of loops in Euclidean space such that these groups are embedded in a Fréchet-Lie group which is the structural group of a princip…
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…
Lie algebras of curves and loop-bundles on surfaces
Juan Alonso, Miguel Paternain, Javier Peraza +1
W. Goldman and V. Turaev defined a Lie bialgebra structure on the -module generated by free homotopy classes of loops of an oriented surface (i.e. the conjugacy classes…
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…
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…
On the classical and quantum Geroch group
Javier Peraza, Miguel Paternain, Michael Reisenberger
The Geroch group is an infinite dimensional transitive group of symmetries of classical cylindrically symmetric gravitational waves which acts by non-canonical transformations on t…