  We study dependence of the atmospheric $\nu_\mu$ and $\bar{\nu}_\mu$ fluxes
on the deviations of the 2-3 mixing from maximal, $|45^\circ - \theta_{23}|$,
on the $\theta_{23}$-octant and on the neutrino mass splitting $\Delta
m_{32}^2$. Analytic expressions for the $\theta_{23}-$deviation effect and the
octant asymmetry are derived. We present conservative estimations of
sensitivities of the iron (magnetized) calorimeter detectors (ICAL) to these
parameters. ICAL can establish the $\theta_{23}$-deviation at higher than
3$\sigma$ confidence level if $| 45^\circ - \theta_{23}| > 6^{\circ}$ with the
exposure of 1 Mton$\cdot$yr. Sensitivity to the octant is low for zero or very
small 1-3 mixing, but it can be substantially enhanced for $\theta_{13} >
3^\circ$. ICAL can measure the difference of $\Delta m_{32}^2$ in $\nu$ and
$\bar\nu$ channels (the CPT test) with accuracy $0.8\times 10^{-4}$ eV$^2$
(3$\sigma$) with 1 Mton$\cdot$yr exposure, and the present MINOS result can be
excluded at $>5\sigma$ confidence level. We discuss possible ways to further
improve sensitivity of the magnetized spectrometers.
