  We study ergodic properties of nonlinear Markov chains and stochastic
McKean-Vlasov equations. For nonlinear Markov chains we obtain sufficient
conditions for existence and uniqueness of an invariant measure and uniform
ergodicity. We also prove optimality of these conditions. For stochastic
McKean-Vlasov equations we establish exponential convergence of their solutions
to stationarity in the total variation metric under
Veretennikov-Khasminskii-type conditions.
