Universal scaling in coupled maps

초록

Using a renormalization method, we study critical scaling behaviors of all period p-tuplings (p=2,3,4,...) in two symmetrically coupled one-dimensional (1D) maps near the symmetry line. We find three (five) kinds of fixed points of a renormalization operator for the case of even (odd) p. The relevant "coupling eigenvalues" associated with coupling perturbations vary depending on the kind of fixed point, while the relevant eigenvalue associated with scaling of the nonlinearity parameter of the uncoupled 1D maps is a common one to all the fixed points. With an example, we also confirm the renormalization results. © 1995 The American Physical Society.