Assertion: period doubling bifurcation | /r/HasProperty | supercritical
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text: We discuss the negative Schwarzian derivative condition in this Section; not only does this condition play a crucial role in deep issues such as understanding precursors to Universality and the question of how smoothness that depends on arbitrary small scale data can have visible effects, but in the context of period doubling, it guaranties that $\mathcal{Q}f^p_{\mu}(x_0)$ is negative for all the period doubling bifurcations for any period $p$ as $\mu$ varies, hence all period doubling bifurcations are supercritical.