Kifer, Yuri Limit theorems in averaging for dynamical systems. (English) Zbl 0841.34048 Ergodic Theory Dyn. Syst. 15, No. 6, 1143-1172 (1995). The ODE system \(dz(t)/dt= \varepsilon B(z(t), f^t y)\) is considered, where \(f^t\) is a so-called suspension flow with the initial condition \(z(0)= x\). The solution of this initial value problem is related to the solution of the averaged system. The main theorem proved in the paper says that under some conditions the difference between the two solutions (divided by \(\varepsilon^{1/2}\)) tends to a Gaussian Markov process that satisfies a certain integral equation as \(\varepsilon\) tends to zero. Several corollaries are also proved. Reviewer: M.Farkas (Budapest) Cited in 9 Documents MSC: 34C29 Averaging method for ordinary differential equations 37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion Keywords:suspension flow; averaged system; Gaussian Markov process PDFBibTeX XMLCite \textit{Y. Kifer}, Ergodic Theory Dyn. Syst. 15, No. 6, 1143--1172 (1995; Zbl 0841.34048) Full Text: DOI References: [1] DOI: 10.1016/0196-8858(87)90012-1 · Zbl 0637.58013 · doi:10.1016/0196-8858(87)90012-1 [2] DOI: 10.1007/BF02757869 · Zbl 0283.58010 · doi:10.1007/BF02757869 [3] Denker, Dynamical Systems and Ergodic Theory, Banach Center Publications 23 (1989) · Zbl 0695.60026 [4] DOI: 10.1007/BF02096625 · Zbl 0755.60095 · doi:10.1007/BF02096625 [5] DOI: 10.1007/BF02937307 · Zbl 0701.60026 · doi:10.1007/BF02937307 [6] DOI: 10.1007/BF01389848 · Zbl 0311.58010 · doi:10.1007/BF01389848 [7] Borodin, Ann. de L’I. H. P. 31 pp 485– (1995) [8] DOI: 10.1016/0167-7152(93)90012-8 · Zbl 0797.60026 · doi:10.1016/0167-7152(93)90012-8 [9] Billingsley, Convergence of Probability Measures. (1968) · Zbl 0172.21201 [10] Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. (Lecture Notes in Mathematics, 470) (1975) · Zbl 0308.28010 · doi:10.1007/BFb0081279 [11] Arnold, Geometric Methods in the Theory of Ordinary Differential Equations. (1983) · doi:10.1007/978-1-4684-0147-9 [12] DOI: 10.1007/BF01231336 · Zbl 0791.58072 · doi:10.1007/BF01231336 [13] DOI: 10.2307/2001571 · Zbl 0714.60019 · doi:10.2307/2001571 [14] Kato, Perturbation Theory for Linear Operators. pp 1966– · Zbl 0836.47009 [15] DOI: 10.1137/1111018 · Zbl 0168.16002 · doi:10.1137/1111018 [16] DOI: 10.1137/1107036 · Zbl 0119.14204 · doi:10.1137/1107036 [17] DOI: 10.1137/1122003 · Zbl 0375.60033 · doi:10.1137/1122003 [18] Freidlin, Random Perturbations of Dynamical Systems. (1984) · Zbl 0522.60055 · doi:10.1007/978-1-4684-0176-9 [19] DOI: 10.1070/RM1978v033n05ABEH002516 · Zbl 0416.60029 · doi:10.1070/RM1978v033n05ABEH002516 [20] DOI: 10.2307/2373927 · Zbl 0368.54014 · doi:10.2307/2373927 [21] DOI: 10.1017/S0143385700002637 · Zbl 0554.60077 · doi:10.1017/S0143385700002637 [22] Sanders, Averaging Methods in Nonlinear Dynamical Systems. (1985) · Zbl 0586.34040 · doi:10.1007/978-1-4757-4575-7 [23] DOI: 10.1137/1104015 · Zbl 0092.33502 · doi:10.1137/1104015 [24] DOI: 10.1007/BF02105185 · Zbl 0797.58068 · doi:10.1007/BF02105185 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.