Our goal is to find dynamic invariants that completely determine elements of the outer automorphism group Out(F_n) of the free group F_n of rank n . To avoid finite order phenomena, we do this for forward rotationless elements. This is not a serious restriction. For example, there is K_n>0 depending only on n such that, for all φ(F_n) , φK_n is forward rotationless. An important part of our analysis is to show that rotationless elements are represented by particularly nice relative train track maps.
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Feighn et al. (2011) studied this question.
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