  One-dimensional Bernoulli mapping with hole is suggested to describe the
regularities of the appearance of a chaotic set under the saddle-node scenario
of the birth of the Smale--Williams hyperbolic attractor. In such a mapping, a
non-trivial chaotic set (with non-zero Hausdorff dimension) arises in the
general case as a result of a cascade of period-adding bifurcations
characterized by geometric scaling both in the phase space and in the parameter
space. Numerical analysis of the behavior of models demonstrating the
saddle-node scenario of birth of a hyperbolic chaotic Smale--Williams attractor
shows that these regularities are preserved in the case of multidimensional
systems. Limits of applicability of the approximate 1D model are discussed.
