On scenarios of chaos appearance in three-dimensional nonoriented maps

For one-parameter families of three-dimensional nonorientable maps we study scenarios of appearance of strange homoclinic attractors (containing only one fixed point). We describe 4 different scenarios leading to discrete homoclinic nonorientable attractors: correspondingly, of Lorenz and figure-eight types (containing a saddle fixed point), and spiral attractors of two types (containing a saddle-focus fixed point). Some examples of realization of these scenarios in the case of three-dimensional nonorientable generalized Henon maps are given.