Four-neutrino oscillation solutions of the atmospheric neutrino anomaly

In the context of neutrino scenarios characterized by four (three active plus one sterile) neutrino species and by mass spectra with two separated doublets, we analyze solutions to the atmospheric neutrino anomaly which smoothly interpolate between ${\nu }_{\mu }\to {\nu }_{\tau }$ and ${\nu }_{\mu }\to {\nu }_s$ oscillations. We show that, although the Super-Kamiokande data disfavor the pure ${\nu }_{\mu }\to {\nu }_s$ channel, they do not exclude its occurrence, with sizable amplitude, in addition to the ${\nu }_{\mu }\to {\nu }_{\tau }$ channel. High energy muon data appear to be crucial in assessing the relative amplitude of active and sterile neutrino oscillations. It is also qualitatively shown that such atmospheric $\nu$ solutions are compatible with analogous solutions to the solar neutrino problem, which involve oscillations of ${\nu }_e$ in both sterile and active states.