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Entire Functions, in the Classification of Differentiable Germs Tangent to the Identity, in One or Two Variables

Patrick Ahern, Jean-Pierre Rosay
1995 Transactions of the American Mathematical Society  
This paper presents a survey and some (hopefully) new facts on germs of maps tangent to the identity (in R, C, or R2), (maps f defined near 0, such that /(0) = 0, and /'(0) is the identity). Proofs are mostly original. The paper is mostly oriented towards precise examples and the questions of descriptions of members in the conjugacy class, flows, fcth root. It happened that entire functions provide clear and easy examples. However they should be considered just as a tool, not as the main topic.
more » ... as the main topic. For example in Proposition 2 the function z i-» z + z2 should be better thought of as the map (x, y) -> (x + x2 -y2, y + 2xy). As original results we have Proposition 1. Let f(z) = z + Y^y=2ajzi ■ Assume that f is the time t map of
doi:10.2307/2154901 fatcat:gc36qjc6xzahbjjy6laf5zsbba