2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68687We prove an analog of Schmid's $\text{\rm SL}_2$-orbit theorem for a class of variations of mixed Hodge structure which includes logarithmic deformations, degenerations of 1-motives and archimedean heights. In particular, as consequence this theorem, we obtain a simple formula for the asymptotic behavior of the archimedean height of a flat family of algebraic cycles which depends only on the weight filtration and local monodromy.57 pages, amstexAlgebraic Geometry14D07, 14C30, 14G40text