Absolutely continuous invariant measures for expanding piecewise linear maps
نویسندگان
چکیده
منابع مشابه
Regularity of Absolutely Continuous Invariant Measures for Piecewise Expanding Unimodal Maps
Let f : [0, 1]→ [0, 1] be a piecewise expanding unimodal map of class C, with k ≥ 1, and μ = ρdx the (unique) SRB measure associated to it. We study the regularity of ρ. In particular, points N where ρ is not differentiable has zero Hausdorff dimension, but is uncountable if the critical orbit of f is dense. This improves on a work of Szewc (1984). We also obtain results about higher order diff...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2001
ISSN: 0020-9910
DOI: 10.1007/pl00005797