  The atmospheric neutrino data collected by the Super-Kamiokande experiment
span about four decades in neutrino energy E, and are thus appropriate to probe
the energy dependence of the oscillation wavelength \lambda associated to
nu_mu<--->nu_tau flavor transitions, when these are assumed to explain the
data. Such dependence takes the form \lambda^{-1}\propto E^n in a wide class of
theoretical models, including ``standard'' oscillations due to neutrino mass
and mixing (n=-1), energy-independent oscillations (n=0), and violations of the
equivalence principle or of Lorentz invariance (n=1). We study first how the
theoretical zenith distributions of sub-GeV, multi-GeV, and upward-going muon
events change for different integer values of n. Then we perform a detailed
analysis of the Super-Kamiokande data by treating the energy exponent n as a
free parameter, with unconstrained scale factors for both the amplitude and the
phase of nu_mu<--->nu_tau oscillations. We find a best-fit range n=-0.9 \pm 0.4
at 90% C.L., which confirms the standard scenario (n=-1) as the dominant
oscillation mechanism, and strongly constrains possible concurrent exotic
processes (n \neq -1). In particular, we work out the interesting case of
leading standard oscillations plus subleading terms induced by violations of
special or general relativity principles, and obtain extremely stringent upper
bounds on the amplitude of such violations in the (nu_mu,nu_tau) sector.
