conjugacy of 1-d diffeomorphisms with periodic points

It is shown that the set of heteroclinic orbits between two periodic orbits of saddle-node type induces functional moduli which are completely contained in a new `transition map'. For one-dimensional diffeomorphisms with saddle-node periodic points, two such diffeomorphisms are conjugated if and only if the transition maps of their heteroclinic orbits are the same. An equivalent transition map is given for diffeomorphisms with hyperbolic periodic points, and it is shown that this transition map is an invariant of conjugation. However, in this case the transition map alone is sufficient to guarantee conjugacy only in a limited sense.