For any complex Hénon map HP, a :  x y  �→  P(x) − ay x  , the universal cover of the forward escaping set U+ is biholomorphic to D × C, where D is the unit disk The vertical foliation by copies of C descends to the escaping set itself and makes it a rather rigid object In this note we give evidence of this rigidity by showing that the analytic structure of the escaping set essentially characterizes the Hénon

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