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Dynamics of the monodromies of the fibrations on the magic 3-manifold

We study the magic manifold $N$ which is a hyperbolic and fibered $3$-manifold. We give an explicit construction of a fiber $F_a$ and its monodromy $:F_a \rightarrow F_a$ of the fibration associated to each fibered class $a$ of $N$. Let $δ_g$ (resp. $δ_g^+$) be the minimal dilatation of pseudo-Anosovs (resp. pseudo-Anosovs with orientable invariant foliations) defined on an orientable closed surface of genus $g$. As a consequence of our result, we obtain the first explicit construction of the following pseudo-Anosovs; a minimizer of $δ_7^+$ and conjectural minimizers of $δ_g$ for large $g$.