Mean Convergence of Periodic Pseudotrajectories and Invariant Measures of Dynamical Systemsстатья
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Аннотация:A discrete dynamical system generated by a homeomorphism of a compact manifold isconsidered. A sequence ω_n of periodic ε_n-trajectories converges in the mean as ε_n → 0 if, for any continuous function ϕ, the mean values on the period ϕ(ω_n) converge as n→∞. It is shown that ω_n converges in the mean if and only if there exists an invariant measure μ such that ϕ(ω_n) converges to ∫φdμ. If a sequence ω_n converges in the mean and converges uniformly to a trajectory Tr, then the trajectory Tr is recurrent and its closure is a minimal strictly ergodic set.