Parabolic Bifurcations in Complex Dimension 2

Parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena. In this paper we consider parabolic bifurcations of families of diffeomorphisms in two complex dimensions. Specifically we consider a two variable family of diffeomorphisms $F_ε: M\to M$ given locally by $F_ε(x,y) = (x + x^2 + ε^2+ ..., b_εy+...)$ where $|b_ε|<1$, and the `$...$' terms involve $x$, $y$ and $ε$.

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