Centralisateurs des difféomorphismes de la demi-droite | Zendy

Hélène Eynard-Bontemps | Zendy

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Centralisateurs des difféomorphismes de la demi-droite

Author(s) -

Hélène Eynard-Bontemps

Publication year - 2009

Publication title -

séminaire de théorie spectrale et géométrie

Language(s) - English

Resource type - Journals

eISSN - 2118-9242

pISSN - 1624-5458

DOI - 10.5802/tsg.272

Subject(s) - uncountable set , centralizer and normalizer , mathematics , diffeomorphism , combinatorics , group (periodic table) , line (geometry) , pure mathematics , physics , geometry , countable set , quantum mechanics

— 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 Z∞ reduces to the infinite cyclic group generated by f . We present here the main result of [3]: Z∞ can actually be a proper and uncountable (hence dense) subgroup of Z1.

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