Unbounded asymmetry of stretch factors
  A result of Handel-Mosher guarantees that the ratio of logarithms of stretch factors of any fully irreducible automorphism of the free group $F_N$ and its inverse is bounded by a constant $C_N$. In this short note we show that this constant $C_N$ cannot be chosen independent of $N$. 
Spencer Dowdall, Ilya Kapovich, and Christopher J Leininger
math.GR