Moscow Mathematical Journal

Volume 23, Issue 4, October–December 2023 pp. 559–570.

Attractors with Non-Invariant Interior

Authors: Stanislav Minkov (1), Alexey Okunev (2), and Ivan Shilin (3)
Author institution:(1) Brook Institute of Electronic Control Machines, Moscow, Russia
(2) Pennsylvania State University, State College, PA, USA
(3) HSE University, Moscow, Russia

Summary:

We construct an open set of endomorphisms of an arbitrary two-dimensional manifold which have attractors and non-wandering sets with non-invariant interior. This is a notable contrast to the properties of diffeomorphisms, where the interior must be invariant.

2020 Math. Subj. Class. 37C70, 37C20, 37E30, 37D30.

Keywords: Attractors, Milnor attractor, dynamics of endomorphisms.

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