Renormalization Analysis of Intermittency in Two Coupled Maps

The critical behavior for intermittency is studied in two coupled one-dimensional (1D) maps. We find two fixed maps of an approximate renormalization operator in the space of coupled maps. Each fixed map has a common relavant eigenvalue associated with the scaling of the control parameter of the uncoupled one-dimensional map. However, the relevant “coupling eigenvalue” associated with coupling perturbation varies depending on the fixed maps. These renormalization results are also confirmed for a linearly-coupled case.