Jonquières maps and SL(2;C)-cocycles
Résumé
We start the study of the family of birational maps (f α,β) of P 2 C in [12]. For "(α, β) well chosen" of modulus 1 the centraliser of f α,β is trivial, the topological entropy of f α,β is 0, there exist two domains of linearisation : in the first one the closure of the orbit of a point is a torus, in the other one the closure of the orbit of a point is the union of two circles. On P 1 C × P 1 C any f α,β can be viewed as a cocyle ; using recent results about SL(2; C)-cocycles ([1]) we determine the LYAPUNOV exponent of the cocyle associated to f α,β .
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