Classification of C~1 Diffeomorphisms of the Real Line Under C~1 Conjugacy

This note will give some classification results for local and global C~1 diffeomorphisms of R under C~1 conjugacy. For γ=1, 2,…, ∞, ω, let D~γ(0)={f: R→R is C~γ; f’(x)>0, x∈R; and f has 0 asits unique fixed point} (local diffeomorphisms of R). In Refs. [1] and [2], we have considered the existence of smooth embedding flows and the other related problems for f∈D~γ(0). As a result, we prove that the following classifications have some numerical invariants as