We study bifurcation mechanisms of the appearance of hyperchaotic attractors
in three-dimensional maps. We consider, in some sense, the simplest cases when
such attractors are homoclinic, i.e. they contain only one saddle fixed point
and entirely its unstable manifold. We assume that this manifold is
two-dimensional, which gives, formally, a possibility to obtain two positive
Lyapunov exponents for typical orbits on the attractor (hyperchaos). For
realization of this possibility, we propose several bifurcation scenarios of
the onset of homoclinic hyperchaos that include cascades of both supercritical
period-doubling bifurcations with saddle periodic orbits and supercritical
Neimark-Sacker bifurcations with stable periodic orbits, as well as various
combinations of these cascades. In the paper, these scenarios are illustrated
by an example of three-dimensional Mir\'a map.Comment: 40 pages, 24 figure