O'Farrell, Anthony G. and Zaitsev, Dmitri
(2011)
FormallyReversible Maps of C2.
Working Paper.
National University of Ireland Maynooth.
(Unpublished)
Abstract
An element g of a group is called reversible if it is conjugate in the group to its
inverse. This paper is about reversibles in the group G = G2 of formallyinvertible pairs of formal
power series in two variables, with complex coefficients. The main result is a description of the
generic reversible elements of G2. We list two explicit sequences of reversibles which between them
represent all the conjugacy classes of such reversibles.We show that each such element is reversible
by some element of finite order, and hence is the product of two elements of finite even order. Those
elements that may be reversed by an involution are called strongly reversible. We also characterise
these.
We draw some conclusions about generic reversibles in the group G = G2 of biholomorphic germs
in two variables, and about the factorization of formal maps as products of reversibles. Specifically,
each product of reversibles reduces to the product of five.
Item Type: 
Monograph
(Working Paper)

Additional Information: 
Supported in part by the Science Foundation Ireland grant 10/RFP/MTH2878. 
Keywords: 
local holomorphic dynamics; involutions; reversible; iteration; resonances; 
Subjects: 
Science & Engineering > Mathematics 
Item ID: 
3764 
Depositing User: 
Prof. Anthony O'Farrell

Date Deposited: 
19 Jun 2012 15:37 
Publisher: 
National University of Ireland Maynooth 
URI: 

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