There are no ?-finite absolutely continuous invariant measures for multicritical circle maps <sup>*</sup>
نویسندگان
چکیده
It is well-known that every multicritical circle map without periodic orbits admits a unique invariant Borel probability measure which purely singular with respect to Lebesgue measure. Can such leave an infinite, $\sigma$-finite absolutely continuous measure? In this paper, using old criterion due Katznelson, we show the answer question no.
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2021
ISSN: ['0951-7715', '1361-6544']
DOI: https://doi.org/10.1088/1361-6544/ac1a02