Cech cohomology of attractors of discrete dynamical systems

摘要

Let f:R~n →R~n be a homeomorphism and Kan asymptotically stable attractor for f. The aim of this paper is to study when the inclusion of Kin its basin of attraction A(K)induces isomorphisms in ?ech cohomology. We show that (i) this is true if coefficients are taken in Q or Z_p(pprime) and (ii) it is true for integral cohomology if and only if the ?ech cohomology of Kor A(K)is finitely generated. We compute the ?ech cohomology of periodic point free attractors of volume-contracting R~3-homeomorphisms and present applications to quite general models in population dynamics.