Given a group G, the conjugacy problem in G is the problem of giving an
effective procedure for determining whether or not two given elements f, g of G
are conjugate, i.e. whether there exists h belonging to G with fh = hg. This
paper is about the conjugacy problem in the group Diffeo(I) of all
diffeomorphisms of an interval I in R. There is much classical work on the
subject, solving the conjugacy problem for special classes of maps.
Unfortunately, it is also true that many results and arguments known to the
experts are difficult to find in the literature, or simply absent.