Homogenization of Coupled Fast-Slow Systems via Intermediate Stochastic Regularization

  title={Homogenization of Coupled Fast-Slow Systems via Intermediate Stochastic Regularization},
  author={Maximilian Engel and Marios-Antonios Gkogkas and Christian Kuehn},
  journal={arXiv: Dynamical Systems},
In this paper we study fully-coupled fast-slow systems of the form $\dot{x}_\epsilon = a(x_\epsilon,y_\epsilon) +\epsilon^{-1}b(x_\epsilon,y_\epsilon)$, $\dot{y}_\epsilon = \epsilon^{-2}g(x_\epsilon,y_\epsilon)$, where $\epsilon$ is a small parameter and, for every fixed $x$, the fast dynamics are sufficiently chaotic with ergodic invariant measure $\mu_x$ such that $b$ has average zero with respect to $\mu_x$. Results of the form $x_\epsilon \to X$ in the limit $\epsilon\to 0$, where $X… Expand

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