Characterization of topologically transitive attractors for analytic plane flows

Shoptrajanov, Martin; Shekutkovski, Nikita

doi:10.2298/fil1501089s

Cited by 2 publications

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“…The papers [8,21], and [23] contain explicit applications of intrinsic shape from [15] to dynamical systems and show the advantage of the intrinsic approach to shape when dealing with dynamical systems.…”

Section: Applications Of Intrinsic Shape In Dynamical Systemsmentioning

confidence: 99%

“…In [25] V. Jiménez López and J. Libre gave a nice topological characterization of the ω-limit set for analytic plane flows. Using this result, a partial answer to the problems involving the characterization of topologically transitive attractors for plane flows is given in [8]. Also, a new proof of the well-known theorem [10] is presented which provides a very elegant characterization of attractors on a topological manifold: Theorem 5.…”

Section: Applications Of Intrinsic Shape In Dynamical Systemsmentioning

confidence: 99%

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Intrinsic Shape Property of Global Attractors in Metrizable Spaces

Shekutkovski¹,

Shoptrajanov²

2020

Nelin. Dinam.

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This paper concerns the connection between shape theory and attractors for semidynamical systems in metric spaces. We show that intrinsic shape theory from [6] is a convenient framework to study the global properties which the attractor inherits from the phase space. Namely, following [6] we'll improve some of the previous results about the shape of global attractors in arbitrary metrizable spaces by using the intrinsic approach to shape which combines continuity up to a covering and the corresponding homotopies of first order.

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Section: Applications Of Intrinsic Shape In Dynamical Systemsmentioning

confidence: 99%

Section: Applications Of Intrinsic Shape In Dynamical Systemsmentioning

confidence: 99%