Abstract
An analysis is presented of the behaviour of the hydrodynamic modes in a horizontal cholesteric layer subjected to a temperature gradient which, when reaching a critical value, drives the system into convective instability. It is found that, because of the mode coupling induced by the external force, the frequency of one of the modes of the system, corresponding to a thermal conduction-orientation mode, goes to zero when the temperature gradient increases up to a critical value. When the cholesteric pitch depends weakly on temperature, only the imaginary part of the frequency vanishes at the instability, and one finds oscillating convection cells

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