Invariant measures for non-contracting multi-valued mappings of the circle

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.

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Bibliographic Details
Published in:Moscow University mathematics bulletin 2010-06, Vol.65 (3), p.124-126
Main Author: Gorbachev, A. N.
Format: Article
Language:English
Subjects:
Analysis
Brief Communications
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0027-1322
1934-8444
DOI:10.3103/S0027132210030083