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Nikita Shekutkovski

1000 Skopje, Republic of Macedonia
Sts. Cyril and Methodius University


Shoptrajanov M., Shekutkovski N.
Shape-invariant Neighborhoods of Nonsaddle Sets
2020, vol. 25, no. 6, pp.  581-596
Asymptotically stable attractors are only a particular case of a large family of invariant compacta whose global topological structure is regular. We devote this paper to investigating the shape properties of this class of compacta, the nonsaddle sets. Stable attractors and unstable attractors having only internal explosions are examples of nonsaddle sets. The main aim of this paper is to generalize the well-known theorem for the shape of attractors to nonsaddle sets using the intrinsic approach to shape which combines continuity up to a covering and the corresponding homotopies of first order.
Keywords: shape, intrinsic shape, attractor, nonsaddle set, regular covering, proximate sequence, Lyapunov function
Citation: Shoptrajanov M., Shekutkovski N.,  Shape-invariant Neighborhoods of Nonsaddle Sets, Regular and Chaotic Dynamics, 2020, vol. 25, no. 6, pp. 581-596
Shekutkovski N.
One Property of Components of a Chain Recurrent Set
2015, vol. 20, no. 2, pp.  184-188
For flows defined on a compact manifold with or without boundary, it is shown that the connectivity components of a chain recurrent set possess a stronger connectivity known as joinability (or pointed 1-movability in the sense of Borsuk). As a consequence, the Vietoris–van Dantzig solenoid cannot be a component of a chain recurrent set, although the solenoid appears as a minimal set of a flow.
Keywords: chain recurrent set, continuity in a covering, pointed 1-movability, joinability
Citation: Shekutkovski N.,  One Property of Components of a Chain Recurrent Set, Regular and Chaotic Dynamics, 2015, vol. 20, no. 2, pp. 184-188

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