C^k 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 a functional modulus. For one-dimensional C^2 diffeomorphisms with saddle-node periodic points, two such diffeomorphisms are C^2 conjugated if and only if the moduli of their heteroclinic orbits are the same. The modulus is related to the global bifurcation associated with disappearance of a saddle-node point. An equivalent modulus is given for C^k diffeomorphisms with hyperbolic periodic points, and it is shown that this modulus is an invariant of C^k conjugation. However, in this case the modulus alone is sufficient to guarantee conjugacy only in a limited sense.