Rational maps are $d$-adic Bernoulli

D. Heicklen; C. Hoffman

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Rational maps are $d$-adic Bernoulli

D. Heicklen·C. Hoffman

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Abstract

Freire, Lopes and Mane proved that for any rational map f there exists a natural invariant measure μ_f [5]. Mane showed there exists an n>0 such that (f^n, μ_f) is measurably conjugate to the one-sided $d^n$-shift, with Bernoulli measure $(\frac 1{d^n},... ,\frac 1{d^n})$ \[15]. In this paper we show that (f,μ_f)is conjugate to the one-sided Bernoulli $d$-shift. This verifies a conjecture of Freire, Lopes and Mane [5] and Lyubich [11].

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BibTeX RIS

D. Heicklen, C. Hoffman. 2004-11-22. Rational maps are $d$-adic Bernoulli. https://arxiv.org/abs/math/0411492

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