Geodesic
Dynamical system of translations in the space of multi-valued functions with closed images
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2012), pp. 28-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the work there is considered the dynamical system of translations in the space $\mathfrak R$ of continuous multi-valued functions with images in complete metric space $(\mathrm{clos}(\mathbb R^n),\rho_\mathrm{cl})$ 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 real-valued 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 $\rho_\mathrm{cl}$ 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. 
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E. A. Panasenko. Dynamical system of translations in the space of multi-valued functions with closed images. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2012), pp. 28-33. http://geodesic.mathdoc.fr/item/VUU_2012_2_a2/

[1] Nemytskii V. V., Stepanov V. V., Kachestvennaya teoriya differentsialnykh uravnenii, GITTL, M., 1949, 550 pp.

[2] Bebutov M. V., “O dinamicheskikh sistemakh v prostranstve nepreryvnykh funktsii”, Byull. In-ta matem. pri MGU, 2:5 (1940), 1–52

[3] Zhukovskii E. S., Panasenko E. A., “Ob odnoi metrike v prostranstve nepustykh zamknutykh podmnozhestv prostranstve $\mathbb R^n$”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2012, no. 1, 15–25

[4] Panasenko E. A., Tonkov E. L., “Invariantnye i ustoichivo invariantnye mnozhestva differentsialnykh vklyuchenii”, Trudy matematicheskogo instituta im. V. A. Steklova, 262, 2008, 202–221 | MR | Zbl

[5] Panasenko E. A., Tonkov E. L., “Rasprostranenie teorem E. A. Barbashina i N. N. Krasovskogo ob ustoichivosti na upravlyaemye dinamicheskie sistemy”, Trudy Instituta matematiki i mekhaniki UrO RAN, 15, no. 3, 2009, 185–201

[6] Panasenko E. A., “O suschestvovanie rekurrentnykh i pochti periodicheskikh reshenii differentsialnogo vklyucheniya”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2010, no. 3, 42–57

[7] Panasenko E. A., Rodina L. I., Tonkov E. L., “Prostranstvo $\mathrm{clcv}(\mathbb R^n)$ s metrikoi Khausdorfa–Bebutova i differentsialnye vklyucheniya”, Trudy Instituta matematiki i mekhaniki UrO RAN, 17, no. 1, 2011, 162–177