The evolution of galaxy clusters can be affected by the repulsion described by the cosmological constant. This conclusion is reached within the modified weak-field General Relativity approach where the cosmological constant Lambda enables to describe the common nature of the dark matter and the dark energy. Geometrical methods of theory of dynamical systems and the Ricci curvature criterion are used to reveal the difference in the instability properties of galaxy clusters which determine their evolutionary paths. Namely, it is shown that the clusters determined by the gravity with Lambda-repulsion tend to become even more unstable than those powered only by Newtonian gravity, the effect to be felt at cosmological time scales.
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