Abstract
We construct the Green current for a random iteration of horizontal-like mappings in 
. This is applied to the study of a polynomial map 
with the following properties:
i. infinity is f-attracting;
ii. f contracts the line at infinity to a point not in the indeterminacy set.
We study for such mappings the escape rates near infinity, i.e. the set of possible values of the function 
We show in particular that the set of possible values can contain an interval.
On the other hand the Green current T of f can be decomposed into pieces associated to an itinerary defined by the indeterminacy points. This allows us to prove that 
exists ||T||-a.e. and we give its value in terms of explicit quantities depending on f.
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Dinh, T., Dujardin, R. & Sibony, N. On the dynamics near infinity of some polynomial mappings in 
.
Math. Ann. 333, 703–739 (2005). https://doi.org/10.1007/s00208-005-0661-3
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DOI: https://doi.org/10.1007/s00208-005-0661-3