  We investigate the imaginary part of the wave vector dependent dynamic spin
susceptibility in Sr$_2$(Ru$_{0.99}$Ti$_{0.01}$)O$_4$ as a function of
temperature using neutron scattering. At T=5 K, two-dimensional incommensurate
(IC) magnetic fluctuations are clearly observed around
$\mathbf{Q}_\text{c}=(0.3,0.3,L)$ up to approximately 60 meV energy transfer.
We find that the IC excitations disperse to ridges around the $(\pi,\pi)$
point. Below 50 K, the energy and temperature dependent excitations are well
described by the phenomenological response function for a Fermi liquid system
with a characteristic energy of 4.0(1) meV. Although the wave vector dependence
of the IC magnetic fluctuations in Sr$_2$(Ru$_{0.99}$Ti$_{0.01}$)O$_4$ is
similar to that in the Fermi liquid state of the parent compound,
Sr$_2$RuO$_4$, the magnetic fluctuations are clearly suppressed by the
Ti-doping.
