  We present spatially resolved distributions and kinematics of the stars and
molecular gas in the central 320pc of NGC1097. The stellar continuum confirms
the previously reported 3-arm spiral pattern extending into the central 100pc.
The stellar kinematics and the gas distribution imply this is a shadowing
effect due to extinction by gas and dust in the molecular spiral arms. The
molecular gas kinematics show a strong residual (i.e. non-circular) velocity,
which is manifested as a 2-arm kinematic spiral. Linear models indicate that
this is the line-of-sight velocity pattern expected for a density wave in gas
that generates a 3-arm spiral morphology. We estimate the inflow rate along the
arms. Using hydrodynamical models of nuclear spirals, we show that when
deriving the accretion rate into the central region, outflow in the disk plane
between the arms has to be taken into account. For NGC1097, despite the inflow
rate along the arms being ~1.2Msun/yr, the net gas accretion rate to the
central few tens of parsecs is much smaller. The numerical models indicate that
the inflow rate could be as little as ~0.06Msun/yr. This is sufficient to
generate recurring starbursts, similar in scale to that observed, every
20-150Myr. The nuclear spiral represents a mechanism that can feed gas into the
central parsecs of the galaxy, with the gas flow sustainable for timescales of
a Gigayear.
