Geodesic
For almost every tent map, the turning point is typical
Fundamenta Mathematicae, Tome 155 (1998) no. 3, pp. 215-235.

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Let $T_a$ be the tent map with slope a. Let c be its turning point, and $μ_a$ the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, $ʃ g dμ_a = lim_{n → ∞} \frac1n ∑_{i=0}^{n-1} g(T^i_a(c))$. As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.
DOI : 10.4064/fm-155-3-215-235

Henk Bruin 1

1 
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Henk Bruin. For almost every tent map, the turning point is typical. Fundamenta Mathematicae, Tome 155 (1998) no. 3, pp. 215-235. doi : 10.4064/fm-155-3-215-235. http://geodesic.mathdoc.fr/articles/10.4064/fm-155-3-215-235/

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