Automorphisms of elliptic $K3$ surfaces and Salem numbers of maximal   degree
  Using elliptic structures, we show that any supersingular K3 surface of Artin invariant $1$ in characteristic $p \not= 5$, $7$, $13$ has an automorphism the entropy of which is the natural logarithm of a Salem number of degree $22$. 
H\'el\`ene Esnault, Keiji Oguiso and Xun Yu
math.AG