Statistical properties of quadratic polynomials with a neutral fixed point
Statistical properties of quadratic polynomials with a neutral fixed point
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DOI：
10.4171/jems/805
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发表时间：
2012-11
影响因子：
2.6
通讯作者：
A. Avila;D. Cheraghi
中科院分区：
文献类型：
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作者：
A. Avila;D. Cheraghi
本文描述了复平面上二次多项式P_a（z）：=e^{2\pi ai} z+z^2的动力学的统计性质，其中a具有高的返回时间.特别地，我们证明了这些映射在它们的测度论吸引子上是唯一遍历的，并且唯一不变概率是描述Julia集中典型轨道统计行为的物理测度.这证实了一个猜想佩雷斯-马可的独特遍历性的刺猬动力学，在这一类的地图。
We describe the statistical properties of the dynamics of the quadratic polynomials P_a(z):=e^{2\pi a i} z+z^2 on the complex plane, with a of high return times. 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 behavior of typical orbits in the Julia set. This confirms a conjecture of Perez-Marco on the unique ergodicity of hedgehog dynamics, in this class of maps.