In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. To achieve this, we propose a condition which only requires four noises

中文翻译：

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具有退化噪声的真实 Ginzburg-Landau 方程的遍历性和指数混合

在本文中，我们建立了在存在仅作用于四个方向的退化随机强迫的情况下，真实 Ginzburg-Landau 方程的不变测度的存在性、唯一性和吸引力性质。主要挑战是建立对应于该系统的马尔可夫动力学的时间渐近平滑特性。为了实现这一点，我们提出了一个只需要四个噪声的条件