Reversible biholomorphic germs

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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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

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