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On the stability of hyperbolic attractors of systems of differential equations

Abstract

We study small C 1-perturbations of systems of differential equations that have a weakly hyperbolic invariant set. We show that the weakly hyperbolic invariant set is stable even if the Lipschitz condition fails.

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Correspondence to N. A. Begun.

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Original Russian Text © N.A. Begun, V.A. Pliss, J.R. Sell, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 2, pp. 139–148.

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Begun, N.A., Pliss, V.A. & Sell, J.R. On the stability of hyperbolic attractors of systems of differential equations. Diff Equat 52, 139–148 (2016). https://doi.org/10.1134/S0012266116020014

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  • DOI: https://doi.org/10.1134/S0012266116020014

Keywords

  • Linear Subspace
  • Invariant Manifold
  • Lipschitz Condition
  • Unperturbed System
  • Dimensional Simplex