Cech cohomology of attractors of discrete dynamical systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:257

Article

关键词: Cech cohomology;    Attractor;    Basin of attraction;    Homeomorphism;   

DOI  :  10.1016/j.jde.2014.05.055

来源: Elsevier

【 摘 要 】

Let f : R-n -> R-n be a homeomorphism and K an asymptotically stable attractor for f. The aim of this paper is to study when the inclusion of K in its basin of attraction A(K) induces isomorphisms in Cech cohomology. We show that (i) this is true if coefficients are taken in Q or Z(p) (p prime) and (ii) it is true for integral cohomology if and only if the Cech cohomology of K or A(K) is finitely generated. We compute the Cech cohomology of periodic point free attractors of volume-contracting R-3-homeomorphisms and present applications to quite general models in population dynamics. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free