Spaces of cohomologies associated with linear functional equations

Genrich Belitskii, Nikolai Bykov

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let F : X → X be a Ck(X), k = [0, ∞], map on a topological space (smooth manifold) X, A : X → End(Cm) and let {Uα} be an F-invariant covering of X. We introduce spaces of cohomologies associated with {Uα} and an operator T = I - R, where (Rφ)(x) = A(x)φ(F(x)) is a weighted substitution operator in Ck(X). This yields a correspondence between Im T and Im T\Uα and the description of Im T in cohomological terms. In particular, it is proven that for any structurally stable diffeomorphism on a circle and for large enough k, the operator T is semi-Fredholm, and a similar result holds for the substitution operators generated by simple multidimensional maps. On the other hand, we show that, in general, the closures of Im T and Im T|Uα are independent.

Original languageEnglish
Pages (from-to)343-356
Number of pages14
JournalErgodic Theory and Dynamical Systems
Issue number2
StatePublished - 1 Jan 1998

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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