Hyperbolic Sets of Ordinary Differential Equations

  • Ken Palmer
Part of the Mathematics and Its Applications book series (MAIA, volume 501)


In this chapter we develop the theory of hyperbolic sets for flows. First we show that the continuity of the splitting into stable and unstable bundles follows from the other items in the definition. Next we develop the theory of exponential dichotomies for linear differential equations, paying special attention to the roughness theorem. We use the latter to prove that hyperbolic sets are expansive both in a “continuous” way and a “discrete” way. Finally we show that hyperbolic sets are robust under perturbation, our major tool here being Lemma 2.17.


Normal Bundle Implicit Function Theorem Fundamental Matrix Exponential Dichotomy Satisfying Inequality 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Ken Palmer
    • 1
  1. 1.School of Mathematical & Statistical SciencesLa Trobe UniversityBundooraAustralia

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