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We describe the statistical properties of the dynamics of the quadratic polynomials on the complex plane, with of high type. In particular, we show that these maps are uniquely ergodic on their measure-theoretic attractors, and the unique invariant probability is a physical measure describing the statistical behaviour of typical orbits in the Julia set. This confirms a conjecture of P´erez-Marco on the unique ergodicity of hedgehog dynamics, in this class of maps.
Cite this article
Artur Avila, Davoud Cheraghi, Statistical properties of quadratic polynomials with a neutral fixed point. J. Eur. Math. Soc. 20 (2018), no. 8, pp. 2005–2062