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Russia Tambov
Section  Mathematics 
Title  Dynamical system of translations in the space of multivalued functions with closed images 
Author(s)  Panasenko E.A.^{a} 
Affiliations  Tambov State University^{a} 
Abstract  In the work there is considered the dynamical system of translations in the space ${\mathfrak R}$ of continuous multivalued functions with images in complete metric space $\big({\rm clos}({\mathbb R}^n), \rho_{{\rm cl}}\big)$ of nonempty closed subsets of ${\mathbb R}^n.$ The distance between such functions is measured by means of the metric analogous to the Bebutov metric constructed for the space of continuous realvalued functions defined on the whole real line. It is shown that for compactness of the trajectory's closure in ${\mathfrak R}$ it is sufficient to have initial function bounded and uniformly continuous in the $\rho_{{\rm cl}}$ metric. As consequence, it is also proved that the trajectory's closure of a recurrent or an almost periodic motion is compact in ${\mathfrak R}.$ 
Keywords  space of multivalued functions with closed images, dynamical system of translations, closure of trajectory 
UDC  517.938.5, 517.911.5 
MSC  37С99, 34A60 
DOI  10.20537/vm120203 
Received  27 December 2011 
Language  Russian 
Citation  Panasenko E.A. Dynamical system of translations in the space of multivalued functions with closed images, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 2, pp. 2833. 
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