Geodesic
Iterations and groups of formal transformations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 584-588

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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.
Keywords: iteration, functional equations.
Mots-clés : formal transformations 
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     author = {Oleg V. Kaptsov},
     title = {Iterations and groups of formal transformations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a4/}
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Oleg V. Kaptsov. Iterations and groups of formal transformations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 5, pp. 584-588. http://geodesic.mathdoc.fr/item/JSFU_2021_14_5_a4/