  By implementing a charge pumping scheme for one-dimensional aperiodic chains,
we confirm the existence of topological phases in these systems whenever their
finite-size realizations admit inversion symmetry. These phases are usually
characterized by an anomalous edge response as a result of the bulk-boundary
correspondence. We show that these signatures are all present in various
chains, each representing a different class of structural aperiodicity: the
Fibonacci quasicrystal, the Tribonacci quasicrystal, and the Thue-Morse chain.
More specifically, we calculate three quantities: the Berry phase of the
crystalline approximation of the finite-size systems, the polarization response
to an inifintesimal static and constant electric field in systems with open
boundary conditions, and the degeneracy of the entanglement spectrum. We find
that all of them provide signatures of a topologically nontrivial phase.
