Abstract

Dynamical systems on manifolds with and without boundary have drastically different features. Attractors of boundary preserving maps may have quite counterintuitive properties: be Lyapunov unstable, have intermingled attracting basins and positive Lebesgue measure. For a long time a groundbreaking example of Itai Kan (1994) developed by Milnor and Bonifant was the main achievement in the field. This example provided Lyapunov unstable attractors with intermingled attracting basins. Recently some new examples and generic properties of attractors of boundary preserving maps were found by the speaker and his students: A. Goodetski, V. Kleptsyn, A. Negut, P. Saltykov, D. Volk. The survey of these results, addressed to a broad audience will be presented in the talk.