Geodesic
Statistical properties of quadratic polynomials with a neutral fixed point
Journal of the European Mathematical Society, Tome 20 (2018) no. 8, pp. 2005-2062

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We describe the statistical properties of the dynamics of the quadratic polynomials Pα​(z)=e2παiz+z2 on the complex plane, with α 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 Pérez–Marco on the unique ergodicity of hedgehog dynamics, in this class of maps.
DOI : 10.4171/jems/805
Classification : 37-XX, 28-XX, 30-XX
Keywords: Small divisors, statistical behaviour, unique ergodicity, hedgehog dynamics, small cycles 
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     author = {Artur Avila and Davoud Cheraghi},
     title = {Statistical properties of quadratic polynomials with a neutral fixed point},
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     pages = {2005--2062},
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     doi = {10.4171/jems/805},
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Artur Avila; Davoud Cheraghi. Statistical properties of quadratic polynomials with a neutral fixed point. Journal of the European Mathematical Society, Tome 20 (2018) no. 8, pp. 2005-2062. doi: 10.4171/jems/805

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