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O'Farrell, Anthony G. and Ahern, Patrick (2009) Reversible biholomorphic germs. Computational Methods and Function Theory, 9 (2). pp. 473-484. ISSN 1617-9447
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Official URL: http://www.heldermann.de/CMF/CMF09/CMF092/cmf09032...
Abstract
Let G be a group. We say that an element f ∈ G is reversible in G if it is conjugate to its inverse, i.e. there exists g ∈ G such that g−1 fg = f−1. We denote the set of reversible elements by R(G). For f ∈ G, we denote by
Rf(G)the set (possibly empty) of reversers of f, i.e. the set of g ∈ G such that g−1fg = f−1. We characterise the elements of R(G) and describe each Rf(G), where G is the the group of biholomorphic germs in one complex variable.
That is, we determine all solutions to the equation f o g o f = g, in which f and g are holomorphic functions on some neighbourhood of the origin, with f(0) = g(0) = 0 and f'(0) ≠ 0 6 ≠ g' (0).
| Item Type: | Article |
|---|---|
| Keywords: | Centralisers; Reversible; Biholomorphic germs; Conjugacy; Group. |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 1806 |
| Identification Number: | EC96E595944846CCA4BDDD43F7222CA4 |
| Depositing User: | Prof. Anthony O'Farrell |
| Date Deposited: | 25 Jan 2010 12:33 |
| Journal or Publication Title: | Computational Methods and Function Theory |
| Publisher: | Heldermann Verlag |
| Refereed: | No |
| Funders: | SFI RFP05/MAT0003, ESF Network HCAA |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/1806 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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