2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156336We study the asymptotics of a family of link invariants on the orbits of a smooth volume-preserving ergodic vector field on a compact domain of the 3-space. These invariants, called linear saddle invariants, include many concordance invariants and generate an infinite-dimensional vector space of link invariants. In contrast, the vector space of asymptotic linear saddle invariants is 1-dimensional, generated by the asymptotic signature. We also relate the asymptotic slice genus to the asymptotic signature.12 pages, 6 figuresGeometric TopologyDynamical Systems57M27, 37A05text