Compact noncontraction semigroups of affine operators

A. S. Voynov   ; V. Yu. Protasov

Sbornik. Mathematics, Tome 206 (2015) no. 7, pp. 921-940

Résumé

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. Bibliography: 32 titles.

Détail

Keywords: affine operator, self-similarity, spectral radius
Mots-clés : partition, primitive matrix.

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