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Regular version of the site

Book chapter

Attractors and skew products

P. 155-175.
Ilyashenko Y., Shilin I.

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.

In book

Edited by: A. Katok, Y. Pesin, F. R. Hertz. Vol. 692: Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov. Providence; Rhode Island: American Mathematical Society, 2017.