Preservation of the convergence of trajectories under small perturbations of hyperbolic mappings of manifolds with boundary

A theorem is proved regarding the preservation of the convergence of trajectories under small perturbations of hyperbolic mappings, possessing a strict Lyapunov function. This result is applied to some models in population genetics.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 82–86, 1988.