  Cold neutron triple-axis measurements have been used to investigate the
nature of the long-wavelength spin dynamics in strongly-doped
La$_{1-x}$Sr$_{x}$MnO$_3$ single crystals with $x$=0.2 and 0.3. Both systems
behave like isotropic ferromagnets at low T, with a gapless ($E_0 < 0.02$ meV)
quadratic dispersion relation $E = E_0 + Dq^2$. The values of the spin-wave
stiffness constant $D$ are large ($D_{T=0}$ = 166.77 meV$ \AA^2$ for $x$=0.2
and D$_{T=0}$ = 175.87 meV$ \AA^2$ for $x$=0.3), which directly shows that the
electron transfer energy for the $d$ band is large. $D$ exhibits a power law
behavior as a function of temperature, and appears to collapse as T -> T_C.
Nevertheless, an anomalously strong quasielastic central component develops and
dominates the fluctuation spectrum as T -> T_C. Bragg scattering indicates that
the magnetization near $T_C$ exhibits power law behavior, with $\beta \simeq
0.30$ for both systems, as expected for a three-dimensional ferromagnet.
