Instability of closed orbits obtained by minimization Ureña Alcázar, Antonio Jesús s: instability, minimizing orbits, symmetries We study the dynamics around closed orbits of autonomous Lagrangian systems. When the configuration space is two-dimensional and orientable we show that every closed orbit minimizing the free-period action functional is orbitally unstable. This result applies even when the minimizers are degenerate or nonisolated, but a particularly strong form of instability holds in the isolated case. Under some symmetry assumptions, free-period action minimizers are unstable also in the higher-dimensional case. Applications to geodesics and celestial mechanics are given. 2025-01-17T07:08:38Z 2025-01-17T07:08:38Z 2022 journal article https://hdl.handle.net/10481/99451 https://doi.org/10.1088/1361-6544/ac8264 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional