Towards scenarios of chaos appearance in three-dimensional maps

We study questions of chaotic dynamics of three-dimensional smooth maps (diffeomorphisms). We show that there exist two main scenarios of chaos developing from a stable fixed point to strange attractors of various types: a spiral attractor, a Lorenz-like strange attractor or a «figure-8» attractor. We give a qualitative description of these attractors and define certain condition when these attractors can be «genuine» ones (pseudohyperbolic strange attractors). We include also the corresponding results of numerical analysis of attractors in three-dimensional Hénon maps.