arXiv subjects
Publications and source records attributed to Eddaly Guerra-Velasco.
In this article, we show that the $N$-center problem with rational weak and moderate forces is not rationally integrable for all but a finite number of values $α\in(0,2)\cap \mathbb{Q}$, where $α$ is the order of the singularities. We identify the remaining cases and provide the necessary conditions for their integrability.
Given a semi-Riemannian manifold $(M,\langle \cdot,\cdot\rangle_g),$ we use the transnormal functions defined on $M$ to reduce fully nonlinear first order PDEs of the form \[ F(x,u,\langle \nabla_g u, \nabla_g u \rangle_g) = 0,\qquad \text{on }M \] into ODEs and obtain local existence results of solutions which are constant along the level sets of the transnormal functions. In particular, we apply this reduction method to obtain new solutions to eikonal equations with a prescribed geometry.
The main goal of this paper is to construct Mather measures for space-time periodical nonconvex Hamiltonians.