On the centralizer of diffeomorphisms of the half-line

• Autores: Hélène Eynard
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 86, Nº 2, 2011, págs. 415-435
• Idioma: inglés
• DOI: 10.4171/cmh/229
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• Resumen

  • Let f be a smooth diffeomorphism of the half-line fixing only the origin and Zr its centralizer in the group of Cr diffeomorphisms. According to well-known results of Szekeres and Kopell, Z1 is a one-parameter group. On the other hand, Sergeraert constructed an f whose centralizer Zr, 2?r??, reduces to the infinite cyclic group generated by f. We show that Zr can actually be a proper dense and uncountable subgroup of Z1 and that this phenomenon is not scarce.