Abstract:
We present necessary and sufficient conditions for the local irreducibility of monotone subhomogeneous transformations of the cone $\mathbb{R}_+^q$. The main attention is paid to the notion of irreducibility of a mapping at zero, which is a weakening of the classical notion of irreducibility of a mapping. We analyze the properties of monotone first-degree positively homogeneous mappings irreducible at zero and of subhomogeneous mappings. Necessary and sufficient conditions are obtained for the primitivity of such mappings.
Keywords:
first-degree positively homogeneous mapping, subhomogeneous mapping, irreducible mapping, irreducible at zero mapping, primitive mapping.
Citation:
V. D. Mazurov, A. I. Smirnov, “Conditions for the irreducibility and primitivity of monotone subhomogeneous mappings”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 3, 2016, 169–177
\Bibitem{MazSmi16}
\by V.~D.~Mazurov, A.~I.~Smirnov
\paper Conditions for the irreducibility and primitivity of monotone subhomogeneous mappings
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 3
\pages 169--177
\mathnet{http://mi.mathnet.ru/timm1332}
\crossref{https://doi.org/10.21538/0134-4889-2016-22-3-169-177}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3555721}
\elib{https://elibrary.ru/item.asp?id=26530890}
Linking options:
https://www.mathnet.ru/eng/timm1332
https://www.mathnet.ru/eng/timm/v22/i3/p169
This publication is cited in the following 3 articles:
A. I. Smirnov, V. D. Mazurov, “Generalization of controls bimodality property in the optimal exploitation problem for ecological population with binary structure”, Optimization and Applications, Optima 2019, Communications in Computer and Information Science, 1145, eds. M. Jacimovic, M. Khachay, V. Malkova, M. Posypkin, Springer, 2020, 206–221
V. D. Mazurov, A. I. Smirnov, “A Criterion for the Existence of Nondestructive Controls in the Problem of Optimal Exploitation of a Binary-Structured System”, Proc. Steklov Inst. Math. (Suppl.), 315:1 (2021), S203–S218
Vl. D. Mazurov, A. I. Smirnov, “O strukture mnozhestva nepodvizhnykh tochek razlozhimykh monotonnykh subodnorodnykh otobrazhenii”, Tr. IMM UrO RAN, 23, no. 4, 2017, 222–231
Citation in format AMSBIB
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