Mathematics – Dynamical Systems
Scientific paper
2009-11-24
Mathematics
Dynamical Systems
24 pages
Scientific paper
Let $f$ be an holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$. We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large metric entropy, close to $\log d^k$. We establish for them strong stochastic properties and prove the positivity of their Lyapunov exponents. Since they have large entropy, those measures are supported in the support of the maximal entropy measure of $f$. They in particular provide lower bounds for the Hausdorff dimension of the Julia set.
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