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Sbornik: Mathematics, 2011, Volume 202, Issue 9, Pages 1285–1302
DOI: https://doi.org/10.1070/SM2011v202n09ABEH004187 (Mi sm7649) 		 
On the structure of invariant measures for set-valued maps

A. N. Gorbachev, A. M. Stepin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (355 kB) Russian version article
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DOI: https://doi.org/10.1070/SM2011v202n09ABEH004187
Abstract: Properties of measures invariant with respect to set-valued maps are studied. It is shown that an absolutely continuous invariant measure for a set-valued map need not be unique, and the set of all invariant measures need not be a Choquet simplex. The problem concerning the existence of invariant measures with respect to set-valued maps parametrized by single-valued and set-valued maps of the circle having various smoothness classes is studied.
Bibliography: 13 titles.
Keywords: set-valued maps, invariant measure, Choquet simplex.
Received: 01.06.2010 and 23.05.2011
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 28B20, 54C60
Language: English
Original paper language: Russian
Citation: A. N. Gorbachev, A. M. Stepin, “On the structure of invariant measures for set-valued maps”, Sb. Math., 202:9 (2011), 1285–1302
Citation in format AMSBIB
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:630
    Russian version PDF:241
    English version PDF:22
    References:70
    First page:28
     
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