论文标题
严重间歇性系统的相关性衰减
Decay of correlations for critically intermittent systems
论文作者
论文摘要
对于具有超吸引固定点的随机间歇性动力系统的家族，我们证明，根据随机性参数和超深固定点上的地图的订单，相位过渡发生在绝对连续不变的概率度量和无限措施之间。如果系统具有绝对连续的不变概率度量，我们表明系统正在混合，即使系统中存在的某些确定性地图具有指数衰减，相关性衰减在多个一级上也是如此。这与其他已知结果对比，其中随机系统采用系统中确定性图的最佳衰减率。
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending on the randomness parameters and the orders of the maps at the superattracting fixed point. In case the systems have an absolutely continuous invariant probability measure, we show that the systems are mixing and that the correlations decay polynomially even though some of the deterministic maps present in the system have exponential decay. This contrasts other known results, where random systems adopt the best decay rate of the deterministic maps in the systems.
