Periodic orbits in a two-variable coupled map

Periodic orbits are calculated for a linear transformation composed of two coupled tent maps using a symbolic dynamics defined as the direct product of the single-map symbols {0,1,2}. As the coupling strength is increased orbits are pruned and a crossover to one-dimensional behavior is observed. The disallowed binary orbits containing only symbols {0,1} form a connected region in a binary symbol plane. Stable orbits may appear for strong couplings.