3 papers
math.AP2026
A Local Linking Theorem for Relativistic Action Functionals
Manuel Garzón, Salvador López-MartÃnez
We establish an analogue of the Brezis-Nirenberg local linking theorem for a class of Szulkin-type functionals arising from relativistic action principles. In this framework, compa…
math.DS2025
Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential
Manuel Garzón, Salvador López-MartÃnez
We establish the existence of non-constant periodic solutions to the Lorentz force equation, where no scalar potential is needed to induce the electromagnetic field. Our results ex…
math.DS2025
Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity
Alberto Enciso, Manuel Garzón, Daniel Peralta-Salas
We prove that, on each low energy level, the natural Hamiltonian system defined by a generic smooth potential on exhibits an arbitrarily high number of hyperbolic pe…