  In periodic quantum systems which are both homogeneously tilted and driven,
the interplay between drive and Bloch oscillations controls transport dynamics.
Using a quantum gas in a modulated optical lattice, we show experimentally that
inhomogeneity of the applied force leads to a rich new variety of dynamical
behaviors controlled by the drive phase, from self-parametrically-modulated
Bloch epicycles to adaptive driving of transport against a force gradient to
modulation-enhanced monopole modes. Matching experimental observations to
fit-parameter-free numerical predictions of time-dependent band theory, we show
that these phenomena can be quantitatively understood as manifestations of an
underlying inhomogeneity-induced phase space structure, in which topological
classification of stroboscopic Poincar\'e orbits controls the transport
dynamics.
