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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V. A. Pliss, Integral Sets of Periodical Systems of Differential Equations (Nauka, Moscow, 1977) [in Russian].
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
- invariant set
- small perturbations
- hyperbolic structures