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Dynamics semi-conjugated to a subshift for some polynomial mappings in C.

Gabriel Vigny — 2007

Publicacions Matemàtiques

We study the dynamics near infinity of polynomial mappings f in C. We assume that f has indeterminacy points and is non constant on the line at infinity L. If L is f-attracting, we decompose the Green current along itineraries defined by the indeterminacy points and their preimages. The symbolic dynamics that arises is a subshift on an infinite alphabet.

Hyperbolic measure of maximal entropy for generic rational maps of k

Gabriel Vigny — 2014

Annales de l’institut Fourier

Let f be a dominant rational map of k such that there exists s < k with λ s ( f ) > λ l ( f ) for all l . Under mild hypotheses, we show that, for A outside a pluripolar set of Aut ( k ) , the map f A admits a hyperbolic measure of maximal entropy log λ s ( f ) with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of f to k + 1 . This provides many examples where non uniform hyperbolic dynamics is established. One of the key tools is to approximate the...

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