Comptes Rendus
Article de recherche - Systèmes dynamiques, Théorie des groupes
Groups acting on the line with at most 2 fixed points: an extension of Solodov’s theorem
[Groupes agissant sur la droite avec au plus 2 points fixes : une extension du théorème de Solodov]
João Carnevale1
1 Instituto de Matemática, Departamento de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Bloco C do Centro de Tecnologia, Térreo, Cidade Universitária, Rio de Janeiro, RJ 21941-909, Brazil
Comptes Rendus. Mathématique, Volume 363 (2025), pp. 951-958

A classical result by Solodov states that if a group acts on the line such that any non-trivial element has at most one fixed point, then the action is either abelian or semi-conjugate to an affine action. We show that the same holds if we relax the assumption, requiring that any non-trivial element has at most 2 fixed points.

Un résultat classique de Solodov stipule que si un groupe agit sur la droite de telle sorte que tout élément non trivial a au plus un point fixe, alors l’action est soit abélienne, soit semi-conjuguée à une action affine. Nous montrons qu’il en va de même si nous relâchons l’hypothèse, en exigeant que tout élément non trivial ait au plus deux points fixes.

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DOI : 10.5802/crmath.777
Classification : 37C85, 57M60, 37B05, 37E05
Keywords: Group actions on the line, affine actions, maps with at most 2 fixed points
Mots-clés : Actions de groupes sur la droite, actions affines, applications avec au plus 2 points fixes

João Carnevale 1

1 Instituto de Matemática, Departamento de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Bloco C do Centro de Tecnologia, Térreo, Cidade Universitária, Rio de Janeiro, RJ 21941-909, Brazil
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Groups acting on the line with at most 2 fixed points: an extension of {Solodov{\textquoteright}s} theorem},
     journal = {Comptes Rendus. Math\'ematique},
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     publisher = {Acad\'emie des sciences, Paris},
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     doi = {10.5802/crmath.777},
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João Carnevale. Groups acting on the line with at most 2 fixed points: an extension of Solodov’s theorem. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 951-958. doi: 10.5802/crmath.777

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