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Talk Abstract

Complex Analysis Techniques for the Hénon Map

Complex Analysis Techniques for the Hénon Map

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
${\Bbb C}$

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.