Examples of strange attractors in three-dimentional nonoriented maps

We consider the problem of existance of discrete strangehomoclinic attractors (i.e. attrators which posess exactly one fixed point) for three-dimensional non-oriented diffeomorphisms. In this article we solve this problem using three-dimensional non-oriented generalized Hénon maps, i.e. polynomial maps with constant and negative Jacobian. We show that such maps can posses non-oriented discrete homoclinic attractors of different types. Herewith the main attention in this work is paid to the description of qualitative and numerical methods which are used to find such attractors (the saddle chart, colored Lyapunov diagram) as well as to the description of attractors’ geometric structures. Examples of various non-oriented strange attractors that were found in specific three-dimensional maps by means of above listed methods are also given.