The complex Hénon map is the complex version of the mapping studied by Hénon,

Besides the well-known relevance of this mapping in the real case, fundamental objects in complex analysis arise from the study of the dynamics of this mapping in ${\Bbb C}$². Examples of such objects are Fatou-Bieberbach domains. (These are proper subsets of ${\Bbb C}$² biholomorphic to ${\Bbb C}$².)

We will describe an analytic method to find the location of homoclinic tangencies and some applications. From the complex analysis perspective, it is important to find such tangencies because close to some of them there are infinitely many Fatou-Bieberbach domains.

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