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Based on a relaxation equation for the second rank alignment tensor characterizing the molecular orientation in liquid crystals, we report on a number of symmetry-breaking transient states and simple periodic and irregular, chaotic out-of-plane orbits under steady flow. Both an intermittency route and a period-doubling route to chaos are found for this five-dimensional dynamic system in a certain range of parameters ͑shear rate, tumbling parameter at isotropic-nematic coexistence, and reduceddoi:10.1103/physreve.66.040702 pmid:12443167 fatcat:gdptckscozfeddd6gwoo6vikgi