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## Compact non-contraction semigrous of affine operators

Sbornik Mathematics. 2015. Vol. 206. No. 7. P. 921-940.
Protasov V. Y., Voinov A. S.

We analyze compact multiplicative semigroups of affine operators acting in a finite-dimensional space. The main result states that every such semigroup is either contracting, that is, contains elements of arbitrarily small operator norm, or all its operators share a common invariant affine subspace on which this semigroup is contracting. The proof uses functional difference equations with contraction of the argument. We look at applications to self-affine partitions of convex sets, the investigation of finite affine semigroups and the proof of a criterion of primitivity for nonnegative matrix families.