Papers by Anthony O'Farrell
arXiv (Cornell University), Nov 21, 2008
Journal D Analyse Mathematique, Dec 1, 1994
Journal of Functional Analysis, Jul 1, 1983
arXiv (Cornell University), Jun 26, 2018
Mathematical proceedings of the Royal Irish Academy, 2022
Mathematische Zeitschrift, 1993
Without Abstract
Mathematische Annalen, Dec 1, 1989
arXiv (Cornell University), Sep 29, 2020
Journal of the London Mathematical Society, Dec 1, 1983
Bulletin of The London Mathematical Society, Sep 1, 1997
American Mathematical Monthly, Aug 1, 1973
Proceedings of the American Mathematical Society, Nov 1, 1990
arXiv (Cornell University), Nov 20, 2008
Let $\Diffeo=\Diffeo(\R)$ denote the group of infinitely-differentiable diffeomorphisms of the re... more Let $\Diffeo=\Diffeo(\R)$ denote the group of infinitely-differentiable diffeomorphisms of the real line $\R$, under the operation of composition, and let $\Diffeo^+$ be the subgroup of diffeomorphisms of degree +1, i.e. orientation-preserving diffeomorphisms. We show how to reduce the problem of determining whether or not two given elements $f,g\in \Diffeo$ are conjugate in $\Diffeo$ to associated conjugacy problems in the subgroup $\Diffeo^+$. The main result concerns the case when $f$ and $g$ have degree -1, and specifies (in an explicit and verifiable way) precisely what must be added to the assumption that their (compositional) squares are conjugate in $\Diffeo^+$, in order to ensure that $f$ is conjugated to $g$ by an element of $\Diffeo^+$. The methods involve formal power series, and results of Kopell on centralisers in the diffeomorphism group of a half-open interval.
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Papers by Anthony O'Farrell