Abstract
In the paper small C 1-perturbations of differential equations are considered. The concepts of a weakly hyperbolic set K and a sheet ϒ for a system of ordinary differential equation are introduced. Lipschitz property is not assumed to hold. It is shown that if the perturbation is small enough, then there is a continuous mapping h: ϒ → ϒY, where ϒY is a sheet of the perturbed system.
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References
V. A. Pliss and G. R. Sell, “Perturbations of Attractors of Differential Equations,” J. Differential Equations 92, 100–124 (1991).
V. A. Pliss and G. R. Sell, “Approximation Dynamics and the Stability of Invariant Sets,” J. Differential Equations 149, 1–51 (1997).
V. A. Pliss, Integral Sets of Periodical Systems of Differential Equations (Nauka, Moscow, 1977) [in Russian].
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Original Russian Text © N.A. Begun, 2012, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2012, No. 4, pp. 3–12.
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Begun, N.A. On the stability of sheet invariant sets of two-dimensional periodic systems. Vestnik St.Petersb. Univ.Math. 45, 145–152 (2012). https://doi.org/10.3103/S1063454112040024
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DOI: https://doi.org/10.3103/S1063454112040024