  Low brightness dips have been recently observed in images of protoplanetary
disks, and they are believed to be shadows by the inner disk. We present
VLT/SPHERE polarimetric differential imaging of the transition disk around the
dipper star RX J1604.3-2130. We gathered 11 epochs that cover a large temporal
baseline, to search for variability over timescales of years, months, weeks,
and days. Our observations unambiguously reveal two dips along an almost
face-on narrow ring (with a width of $\sim$20 au), and the location of the peak
of this ring is at $\sim$65 au. The ring lies inside the ring-like structure
observed with ALMA, which peaks at $\sim$83 au. This segregation can result
from particle trapping in pressure bumps, potentially due to planet(s). We find
that the dips are variable, both in morphology and in position. The eastern
dip, at a position angle (PA) of $\sim$83.7$\pm$13.7$^\circ$, has an amplitude
that varies between 40% to 90%, and its angular width varies from 10$^{\circ}$
to 34$^{\circ}$. The western dip, at a PA of $\sim$265.90$\pm$13.0$^\circ$, is
more variable, with amplitude and width variations of 31% to 95% and
12$^{\circ}$ to 53$^{\circ}$, respectively. The separation between the dips is
178.3$^{\circ}\pm$14.5$^{\circ}$, corresponding to a large misalignment between
the inner and outer disk, supporting the classification of J1604 as an
aperiodic dipper. The variability indicates that the innermost regions are
highly dynamic, possibly due to a massive companion or to a complex magnetic
field topology.
