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Mat. Sb., 2011, Volume 202, Number 9, Pages 35–52 (Mi msb7649)  

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

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7649

Full text: PDF file (566 kB)
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English version:
Sbornik: Mathematics, 2011, 202:9, 1285–1302

Bibliographic databases:

UDC: 517.98
MSC: 28B20, 54C60
Received: 01.06.2010 and 23.05.2011

Citation: A. N. Gorbachev, A. M. Stepin, “On the structure of invariant measures for set-valued maps”, Mat. Sb., 202:9 (2011), 35–52; Sb. Math., 202:9 (2011), 1285–1302

Citation in format AMSBIB
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