  As the normal state sheet resistance, $R_n$, of a thin film superconductor
increases, its superconducting properties degrade. For $R_n\simeq h/4e^2$
superconductivity disappears and a transition to a nonsuperconducting state
occurs. We present electron tunneling and transport measurements on ultrathin,
homogeneously disordered superconducting films in the vicinity of this
transition. The data provide strong evidence that fluctuations in the amplitude
of the superconducting order parameter dominate the tunneling density of states
and the resistive transitions in this regime. We briefly discuss possible
sources of these amplitude fluctuation effects. We also describe how the data
suggest a novel picture of the superconductor to nonsuperconductor transition
in homogeneous 2D systems.
