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On the stability of sheet invariant sets of two-dimensional periodic systems

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

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Correspondence to N. A. Begun.

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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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Keywords

  • stability
  • invariant set
  • small perturbations
  • hyperbolic structures