Izvorni znanstveni članak

https://doi.org/10.3336/gm.42.1.10

Shape properties of the boundary of attractors

J. J. Sánchez-Gabites ; Departamento de Geometria y Topologia, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
José M. R. Sanjurjo ; Departamento de Geometria y Topologia, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain

Sažetak

Let M be a locally compact metric space endowed with a continuous flow φ : M × R → M. Assume that K is a stable attractor for φ and P A(K) is a compact positively invariant neighbourhood of K contained in its basin of attraction. Then it is known that the inclusion K P is a shape equivalence and the question we address here is whether there exists some relation between the shapes of ∂K and ∂P. The general answer is negative, as shown by example, but under certain hypotheses on K the shape domination Sh(∂K) ≥ Sh(∂P) or even the equality Sh(∂K) = Sh(∂P) hold. However we also put under study interesting situations where those hypotheses are not satisfied, albeit other techniques such as Lefschetz's duality render results relevant to our question.

Ključne riječi

Dynamical systems; attractors; boundary of attractors; shape

Hrčak ID:

12889

URI

https://hrcak.srce.hr/12889

Datum izdavanja:

12.6.2007.

Posjeta: 1.295 *