2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70680We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we establish sharp uniform lower bounds of this invariant for the following classes of symplectomorphisms of cotangent bundles over a compact base: 1) non-identical compactly supported symplectomorphisms which are symplectically isotopic to the identity, 2) symplectomorphisms generated by classical Hamiltonian functions, 3) Dehn twist like symplectomorphisms over compact rank one symmetric spaces.46 pages, 3 figuresSymplectic GeometryDynamical Systemstext