The geometry of generalized loxodromic elements

We explore geometric conditions which ensure a given element of a finitely
generated group is, or fails to be, generalized loxodromic; as part of this we
prove a generalization of Sisto's result that every generalized loxodromic
element is Morse. We provide a sufficient geometric condition for an element of
a small cancellation group to be generalized loxodromic in terms of the
defining relations and provide a number of constructions which prove that this
condition is sharp.