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math.DS2022
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…
math.GT2022
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…