In this paper we consider diffeomorphisms of ℂ2 of the special form F(z,w) = (w,-z + 2G(w)). For such maps the origin is a parabolic fixed point. Under certain hypotheses on G we prove the existence of a domain Ω ⊂ ℂ with 0 ∈ ∂Ω and of invariant complex curves w = f(z) and w = g(z), z ∈ Ω, for F-1 and F, such that F-n(z,f(z)) → 0 and Fn(z,g(z)) → 0 as n → ∞.
|Original language||English (US)|
|Number of pages||12|
|Journal||Houston Journal of Mathematics|
|State||Published - Dec 1 1998|
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