| Abstract: |
| In this talk, we study intermittent behaviors of coupled piecewise-expanding map lattices with two nodes and a weak coupling. We show that the successive phase transition between ordered and disordered phases occurs for almost every orbit. That is, we prove that $\lim\sup|x_1(n)-x_2(n)|\geq c_0>0$ and $\lim\inf|x_1(n)-x_2(n)|=0$, as $n\to\infty$, where $x_1(n)$, $x_2(n)$ correspond to coordinates of two nodes at the iterative step $n$. We also prove the same conclusion for weakly coupled tent-map lattices with any multi-node. |
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