Relativistic effects in the dynamics of a particle in a Coulomb field Ortega Ríos, Rafael Rojas, David Bertrand’s property Relativistic oscillator Coulomb’s law Strong integrability This work was financially supported by the Ministerio de Ciencia, Innovación Universidades/Agencia Estatal de Investigación grant numbers PID2021-128418NA-I00 and PID2023-146424NB-I00; and by the Generalitat de Catalunya, Spain grant 2021 SGR 00113. We prove that Bertrand’s property cannot occur in a special-relativistic scenario using the properties of the period function of planar centres. We also explore some integrability properties of the relativistic Coulomb problem and the asymptotic behavior of collision solutions. 2025-02-18T08:11:30Z 2025-02-18T08:11:30Z 2024-08-02 journal article Published version: R. Ortega and D. Rojas. Physica D: Nonlinear Phenomena Volume 472, February 2025, 134534. https://doi.org/10.1016/j.physd.2025.134534 https://hdl.handle.net/10481/102436 10.1016/j.physd.2025.134534 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Elsevier