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Formally-Reversible Maps of C2

O'Farrell, Anthony G. and Zaitsev, Dmitri (2011) Formally-Reversible Maps of C2. Working Paper. National University of Ireland Maynooth. (Unpublished)

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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 formally-invertible 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 & Statistics
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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