Renormalization analysis of two coupled maps

초록

The critical behavior of period-doubling bifurcations is studied in two coupled one-dimensional (1D) maps. We find three fixed maps of an approximate renomalization operator in the space of coupled maps. Each fixed map has a common relevant eigenvalue associated with scaling of the nonlinear parameter of the 1D map. However, relevant "coupling" eigenvalues associated with scaling of the coupling strength parameter vary depending on the fixed maps. The results of the renormalization analysis agree well with numerical results. © 1993.