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Linearization of Nonautonomous Impulsive System with Nonuniform Exponential Dichotomy

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  • Yongfei Gao
  • Yonghui Xia
  • Xiaoqing Yuan
  • P. J. Y. Wong

Abstract

This paper gives a version of Hartman-Grobman theorem for the impulsive differential equations. We assume that the linear impulsive system has a nonuniform exponential dichotomy. Under some suitable conditions, we proved that the nonlinear impulsive system is topologically conjugated to its linear system. Indeed, we do construct the topologically equivalent function (the transformation). Moreover, the method to prove the topological conjugacy is quite different from those in previous works (e.g., see Barreira and Valls, 2006).

Suggested Citation

  • Yongfei Gao & Yonghui Xia & Xiaoqing Yuan & P. J. Y. Wong, 2014. "Linearization of Nonautonomous Impulsive System with Nonuniform Exponential Dichotomy," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnlaaa:860378
    DOI: 10.1155/2014/860378
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