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Ergodic properties of discretizations of dynamical systems. (English. Russian original) Zbl 0589.58012
Sov. Math., Dokl. 30, 449-452 (1984); translation from Dokl. Akad. Nauk SSSR 278, 779-782 (1984).
We investigate the influence of small deterministic perturbations of dynamical systems arising from the discretization of the space, specifically the influence on their asymptotic properties such as existence and stability of periodic trajectories. A typical example of this kind of perturbation is that of the approximation errors, inevitably present when modelling dynamical systems on computers.

37A99 Ergodic theory
37G99 Local and nonlocal bifurcation theory for dynamical systems
11J04 Homogeneous approximation to one number