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. 
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
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