Some phase transitions in coupled map lattices - Keller, Gerhard; Künzle, Martin; Nowicki, Tomasz (Physica D-Nonlinear Phenomena, 1992)
We study finite coupled map lattices of size d ⩾ 2 with individual maps τ: [0, 1] → [0, 1] and constant diffuse coupling. For τ (x) = 2x mod 1 we give sufficient conditions that the coupled system has a continuum of ergodic components. In the case d = 2 we determine the number of ergodic components for all coupling strengths. If τ is a mixing tent map close to the transition from mixing to a periodic interval with period 2, the uncoupled system is mixing, whereas numerical studies suggest that coupling with a suitable strength breaks up the phase space into domains which are interchanged with period 2. In case d = 2 we prove this rigorously.