Parabolic Bifurcations in Complex Dimension 2

Abstract

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 $F_{\epsilon }:M\to M$ given locally by $$F_{\epsilon }(x,y)=(x+x^2+{\epsilon }^2+...,b_{\epsilon }y+...)$$ where $|b_{\epsilon }|<1$, and the `$...$' terms involve $x$, $y$ and $\epsilon$.

25 pages, incl. references