Attractors and skew products
Different notions of attractors and relations between them are considered. The major new result claims that Lyapunov unstable Milnor attractors are topologically generic in a space of diffeomorphisms of any manifold of dimension greater than one. This result is due to the second author. A sketch of the proof is given. New robust properties of diffeomorphisms obtained with the help of the so called Ilyashenko-Gordetski strategy are described.