O'Farrell, Anthony G. and Ahern, Patrick
(2009)
Reversible biholomorphic germs.
Computational Methods and Function Theory, 9 (2).
pp. 473484.
ISSN 16179447
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 
URI: 

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