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Invariant measures exist under a summability condition for unimodal maps. (English) Zbl 0736.58030
Let $$f$$ be a universal $$C^ 3$$-function on the interval with negative Schwarzian derivative. If at the critical value $$c$$ the iterates $$f^ n=f\circ\ldots\circ f$$ of $$f$$ have the property that $$(f^ n)'(f(c))$$ tends to infinity “fast enough” then $$f$$ admits a unique absolutely continuous (w.r.t. the Lebesgue measure) invariant probability measure. This generalizes a result of Collet and Eckmann.

##### MSC:
 37A99 Ergodic theory 37D99 Dynamical systems with hyperbolic behavior 28D20 Entropy and other invariants
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##### References:
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