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We explore the evolution of the eccentricity of an accretion disc perturbedby an embedded planet whose mass is sufficient to open a large gap in the disc.Various methods for representing the orbit-averaged motion of an eccentric discare discussed. We characterize the linear instability which leads to the growthof eccentricity by means of hydrodynamical simulations. We numerically recoverthe known result that eccentricity growth in the disc is possible when theplanet-to-star mass ratio exceeds 0.003. For mass ratios larger than thisthreshold, the precession rates and growth rates derived from simulations, aswell as the shape of the eccentric mode, compare well with the predictions of alinear theory of eccentric discs. We study mechanisms by which the eccentricitygrowth eventually saturates into a non-linear regime.

Secular evolution of eccentricity in protoplanetary discs with gap-opening planets