Bounded Distortion versus Uniformly Summable Derivatives
نویسندگان
چکیده
Let T : X → X be a real analytic full branch expanding map, where X is a compact connected subset of R with non-empty interior. A well known sufficient condition for the existence of a T -invariant probability measure equivalent to Lebesgue measure is that T has bounded distortion. An alternative sufficient condition is that T has uniformly summable derivatives (see [BJ]). The purpose of this note is to show that the bounded distortion condition and the uniformly summable derivatives condition are independent.
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