Geodesic
Conditions for the irreducibility and primitivity of monotone subhomogeneous mappings
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 169-177

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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. 
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     author = {V. D. Mazurov and A. I. Smirnov},
     title = {Conditions for the irreducibility and primitivity of monotone subhomogeneous mappings},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a16/}
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V. D. Mazurov; A. I. Smirnov. Conditions for the irreducibility and primitivity of monotone subhomogeneous mappings. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 169-177. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a16/