We consider a surface bundle over the circle, the so-called magic manifold M. We determine homology classes whose minimal rep-resentatives are genus 0 fiber surfaces for M, and describe their monodromies by braids. Among those classes whose representa-tives have n punctures for each n, we decide which one realizes the minimal entropy. We show that for each n > 9 (resp. n = 3,4,5, 7, 8), there exists a pseudo-Anosov homeomorphism Φ_n :D_n→ D_n with the smallest known entropy (resp. the smallest entropy) which occurs as the monodromy on an n-punctured disk fiber for the Dehn filling of M. A pseudo-Anosov homeomorphism Φ_6 : D_6→D_6 with the smallest entropy occurs as the monodromy on a 6-punctured disk fiber for M.
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