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Talk abstract:
Complex Analysis Techniques for the Hénon Map
Estela Gavosto, University of Kansas
The complex Hénon map is the complex version of the
mapping studied by Hénon,
H(x,y) = (1- ax2 + by,x).
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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