Shape theory and dynamical systems (Q2702164)

This paper begins with an elementary introduction to the theory of shape as introduced by K. Borsuk. A similar section follows giving the basic notions of dynamical systems focused on continuous systems or flows. The paper then covers several topics where shape theory has been successfully applied to dynamical systems. These topics include: the shape of attractors in a flow, the shape of isolated invariant non-saddle sets in a flow, and the Lyusternik-Shnirel'man category of invariant isolated sets. The authors and their colleagues contributed significantly to the research summarized in the latter sections of the paper.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00066].