Symmetric and strongly symmetric homeomorphisms on the real line with non-symmetric inversion

2019/05/15 by Wei, Huaying, Matsuzaki, Katsuhiko
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.05933

Abstract

We show an example of a symmetric homeomorphism h of the real line ℝ onto itself such that h^-1 is not symmetric. This implies that the set of all symmetric self-homeomorphisms of ℝ does not constitute a group under the composition. We also deal with strongly symmetric self-homeomorphisms of ℝ along the same line. These results reveal the difference of the sets of such self-homeomorphisms of the real line from those of the unit circle.

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