Abstract
Two selfmappings and of the open interval are said to be regularly conjugate with respect to the distinguished end-point whenever for some uniformly regularly varying at bijective selfmapping we have . Let denote the (Szekeres–Lundberg) family of fixed point free bijections of , strongly attracting to , with derivative at satisfying , which additionally possess continuous (weakly) increasing principal function , for . All regular conjugacy classes of elements of are constructed in terms of the principal functions, the non-measurable included. A few representatives of different regular conjugacy classes among S–L diffeomorphisms are constructed, too.
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