  We investigate the structure of the characteristic polynomial det(xI-T) of a
transition matrix T that is associated to a train track representative of a
pseudo-Anosov map [F] acting on a surface. As a result we obtain three new
polynomial invariants of [F], one of them being the product of the other two,
and all three being divisors of det(xI-T). The degrees of the new polynomials
are invariants of [F ] and we give simple formulas for computing them by a
counting argument from an invariant train track. We give examples of genus 2
pseudo-Anosov maps having the same dilatation, and use our invariants to
distinguish them.
