## Abstract

Let F : X → X be a C^{k}(X), k = [0, ∞], map on a topological space (smooth manifold) X, A : X → End(C^{m}) 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 C^{k}(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 language | English |
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Pages (from-to) | 343-356 |

Number of pages | 14 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 1998 |

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics