Hyperbolic measure of maximal entropy for generic rational maps of
Gabriel Vigny (2014)
Annales de l’institut Fourier
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Let be a dominant rational map of such that there exists with for all . Under mild hypotheses, we show that, for outside a pluripolar set of , the map admits a hyperbolic measure of maximal entropy with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of to . This provides many examples where non uniform hyperbolic dynamics is established. One of the key tools is to approximate...