Shape-invariant neighborhoods of nonsaddle sets (Q2235110)

The paper addresses the shape properties of a class of compact and non-saddle sets. Asymptotically stable attractors and unstable attractors with no external explosions are examples of non-saddle sets. The authors introduce and thoroughly study the local shape properties of an isolated invariant non-saddle set using the intrinsic approach to shape which combines continuity up to a covering and the corresponding homotopies of first order. The highlights of the paper are: intrinsic shape for compact metric spaces, basic notions and results on dynamical systems, topological aspects of non-saddle sets, symbolical analysis on a class of non-saddle sets. The discussion underlines the focus points with several examples of systems of differential equations in the two-dimensional plane.