Smoothness repaired by iteration

• DOI: 10.1007/s00010-014-0277-3
• Publication Date: 2014-07-22T03:42:42Z
• Authors: Xiaohua Liu; Liu Liu; Weinian Zhang
• Keywords: Smoothness

It is easy to find some nonsmooth functions whose iterates are smooth ones, showing that iteration can change nonsmoothness into smoothness. In order to investigate the change and avoid complicated computation, in this paper we classify piecewise C1 self-mappings on the compact interval [0, 1] each of which has only one nonsmooth point. We give necessary and sufficient conditions under which the second order iterates are C1 smooth functions.