Iterations and groups of formal transformations

2020/08/19 by O. V. Kaptsov, Kaptsov, O. V. · 1 citation
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #math.DS #math.GR #nlin.CD

paper · pdf · doi:10.48550/arxiv.2008.08429

6 pages

arxiv created 2020/08/19 · arxiv updated 2020/08/20

Abstract

In this paper, we consider the problem of formal iteration. We construct an area preserving mapping which does not have any square root. This leads to a counterexample to Moser's existence theorem for an interpolation problem. We give examples of formal transformation groups such that the iteration problem has a solution for every element of the groups.

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