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In this survey paper, we report on recent works concerning exactobservability (and, by duality, exact controllability) properties ofsubelliptic wave and Schr{\"o}dinger-type equations. These results illustratethe slowdown of propagation in directions transverse to the horizontaldistribution. The proofs combine sub-Riemannian geometry, semi-classicalanalysis, spectral theory and non-commutative harmonic analysis.

Exact observability properties of subelliptic wave and Schr{\"o}dinger equations