Geodesic
On the structure of invariant measures for set-valued maps
Sbornik. Mathematics, Tome 202 (2011) no. 9, pp. 1285-1302

Voir la notice de l'article provenant de la source Math-Net.Ru

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
Mots-clés : Choquet simplex. 
@article{SM_2011_202_9_a1,
     author = {A. N. Gorbachev and A. M. Stepin},
     title = {On the structure of invariant measures for set-valued maps},
     journal = {Sbornik. Mathematics},
     pages = {1285--1302},
     publisher = {mathdoc},
     volume = {202},
     number = {9},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_9_a1/}
}
TY  - JOUR
AU  - A. N. Gorbachev
AU  - A. M. Stepin
TI  - On the structure of invariant measures for set-valued maps
JO  - Sbornik. Mathematics
PY  - 2011
SP  - 1285
EP  - 1302
VL  - 202
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2011_202_9_a1/
LA  - en
ID  - SM_2011_202_9_a1
ER  - 
%0 Journal Article
%A A. N. Gorbachev
%A A. M. Stepin
%T On the structure of invariant measures for set-valued maps
%J Sbornik. Mathematics
%D 2011
%P 1285-1302
%V 202
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2011_202_9_a1/
%G en
%F SM_2011_202_9_a1
A. N. Gorbachev; A. M. Stepin. On the structure of invariant measures for set-valued maps. Sbornik. Mathematics, Tome 202 (2011) no. 9, pp. 1285-1302. http://geodesic.mathdoc.fr/item/SM_2011_202_9_a1/