Wg. Li et Mr. Zhang, RIGIDITY RESULT ON CONJUGACIES OF FAMILIES OF DIFFEOMORPHISMS, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 40(10), 1997, pp. 1036-1044
Embedding flows are used to obtain a rigidity result on strongly topol
ogical conjugacy of families of diffeomorphisms, i.e. families of C-r
(2 less than or equal to r less than or equal to infinity) diffeomorph
isms, the strongly topologically conjugating homeomorphisms near degen
erate saddle-nodes will be differentiable on center manifolds of the s
addle-nodes.