2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72014This is a survey on natural local torus actions which arise in integrable dynamical systems, and their relations with other subjects, including: reduced integrability, local normal forms, affine structures, monodromy, global invariants, integrable surgery, convexity properties of momentum maps, localization formulas, integrable PDEs.Paper written for a book edited by Bolsinov, Fomenko and OshemkovDynamical SystemsMathematical Physics37J35,53D20,37G05,70K45,34C14text