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.
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