Most expanding maps have no absolutely continuous invariant measure
نویسندگان
چکیده
منابع مشابه
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If f is a measurable transformation of a Lebesgue measure space (X,A, λ) to itself, that does not preserve the measure λ, one can study the invariant measures of f and compare them to λ. A especially interesting case is when f is non-singular with respect to λ (in the sense thatλ(A) = 0 iff λ( f(A)) = 0), but nevertheless there exist no σ-finite invariant measure which is absolutely continuous ...
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Let M be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension d ≥ 1. Let m be some (smooth) volume probability measure in M. Let C(M,M) be the set of C maps M → M, endowed with the C topology. Given f ∈ C(M,M), we say that μ is an acim for f if μ is an f -invariant probability measure which is absolutely continuous with respect to m. Theorem 1. The set R of C map...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1999
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-134-1-69-78