  We study topological charge pumping in one-dimensional quasiperiodic systems.
Since these systems lack periodicity, we cannot use the conventional approach
based on the topological Chern number defined in the momentum space. Here, we
develop a general formalism based on a real space picture using the so-called
Bott index. We extend the Bott index that was previously used to characterize
quantum Hall effects in quasiperiodic systems, and apply it to topological
charge pumping in quasiperiodic systems. The Bott index allows us to
systematically compute topological indices of charge pumping, regardless of the
detail of quasiperiodic models. We apply this formalism to the
Fibonacci-Rice-Mele model which we made from Fibonacci lattice, a well-known
quasiperiodic system, and Rice-Mele model. We find that these quasiperiodic
systems show topological charge pumping with a multi-level behavior due to the
fractal nature of the Fibonacci lattice. Such multi-level pumping behaviors can
be understood by a real space renormalization group analysis.
