We determine the smallest stretch factor among pseudo-Anosov maps with an
orientable invariant foliation on the closed nonorientable surfaces of genus
,
,
,
,
,
,
,
,
,
and
. We
also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov
map with orientable invariant foliations on the closed orientable surfaces of genus
,
,
,
,
and .
As a byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a
nonorientable surface or an orientation-reversing pseudo-Anosov map on an
orientable surface does not have Galois conjugates on the unit circle. This shows that
the techniques that were used to disprove Penner’s conjecture on orientable surfaces
are ineffective in the nonorientable cases.
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