An introduction to classical monodromy: applications to molecules in external fields Omiste, Juan J. González Férez, María Rosario Ortega Ríos, Rafael J.J.O. acknowledges the funding from Juan de la Cierva - Incorporación program granted by Ministerio de Ciencia e Innovación (Spain) and Project PID2019-106732GB-I00 (MINECO). R.G.F. acknowledges financial support by the Spanish Project No. FIS2017-89349-P (MINECO), and by the Andalusian research group FQM- 207. This study has been partially financed by the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía and European Regional Development Fund (ERDF), Ref. SOMM17/6105/UGR. R.G.F. completed some of this work as a Fulbright fellow at ITAMP at Harvard University. An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. As a prototype of classical monodromy with azimuthal symmetry, we consider a linear molecule interacting with external fields and explore the topology structure of its phase space. Based on the behavior of closed orbits around singular points or regions of the energy-momentum plane, a semitheoretical method is derived to detect classical monodromy. The validity of the monodromy test is numerically illustrated for several systems with azimuthal symmetry. 2022-04-25T07:16:47Z 2022-04-25T07:16:47Z 2022-03-08 info:eu-repo/semantics/article Published version: J. Math. Phys. 63, 032702 (2022); [doi: 10.1063/5.0079354] http://hdl.handle.net/10481/74507 10.1063/5.0079354 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España