Invariant Measures for Non-Contracting Multi-Valued Mappings of the Circle / Gorbachev A.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 3. P. 46-48 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 124-126].
The problem of existence of an absolutely continuous invariant measure for non-contracting multi-valued mappings of the circle is considered. It is shown that the existence of finite or infinite invariant measures depends on the differentiability class of the multi-valued mapping.
multivalued mapping, absolute continuous
invariant measure, differentiability class, infinite measure.