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Article Contents

# New examples of S-unimodal maps with a sigma-finite absolutely continuous invariant measure

• We combine the technique of inducing with a method of Johnson boxes and construct new examples of S-unimodal maps $\varphi$ which do not have a finite absolutely continuous invariant measure, but do have a $\sigma$-finite one which is infinite on every non-trivial interval.
We prove the following dichotomy. Every absolutely continuous invariant measure is either $\sigma$-finite, or else it is infinite on every set of positive Lebesgue measure.
Mathematics Subject Classification: Primary: 37E05; Secondary: 28D05, 37C40.

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