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Mat. Sb., 2015, Volume 206, Number 7, Pages 33–54 (Mi msb8408)  

This article is cited in 3 scientific papers (total in 3 papers)

Compact noncontraction semigroups of affine operators

A. S. Voynov, V. Yu. Protasov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00332
13-01-00642
Dynasty Foundation
Simons Foundation
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
The work of the first author was supported by the Russian Foundation for Basic Research (grant no. 14-01-00332), the "Dynasty" Foundation, a Simons-IUM Fellowship, and by the Council of the President of the Russian Federation for the Support of Leading Scientific Schools (grant no. НШ-3682.2014.1); the work of the second author was supported by the Russian Foundation for Basic Research (grant nos. 13-01-00642 and 14-01-00332) and the "Dynasty" Foundation.


DOI: https://doi.org/10.4213/sm8408

Full text: PDF file (618 kB)
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English version:
Sbornik: Mathematics, 2015, 206:7, 921–940

Bibliographic databases:

Document Type: Article
UDC: 517.98+514.172.4+514.174.5
MSC: 52B45, 52C07
Received: 21.07.2014 and 11.02.2015

Citation: A. S. Voynov, V. Yu. Protasov, “Compact noncontraction semigroups of affine operators”, Mat. Sb., 206:7 (2015), 33–54; Sb. Math., 206:7 (2015), 921–940

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. A. Al'pin, V. S. Al'pina, “Combinatorial structure of $k$-semiprimitive matrix families”, Sb. Math., 207:5 (2016), 639–651  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. M. V. Berlinkov, M. Szykula, “Algebraic synchronization criterion and computing reset words”, Inf. Sci., 369 (2016), 718–730  crossref  isi  scopus
    3. Gerencser B., Gusev V.V., Jungers R.M., “Primitive Sets of Nonnegative Matrices and Synchronizing Automata”, SIAM J. Matrix Anal. Appl., 39:1 (2018), 83–98  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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