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Nonlinear Oscillations

, Volume 9, Issue 2, pp 274–279 | Cite as

Relationship between invariant sets of systems of differential equations and the corresponding difference equations

  • A. M. Tkachuk
Article
  • 25 Downloads

Abstract

We study the relationship between invariant sets of systems of differential equations and the corresponding difference equations in terms of sign-constant Lyapunov functions. For systems of differential equations, we obtain a converse result concerning the existence of a positive-definite Lyapunov function whose zeros coincide with a given invariant manifold.

Keywords

Difference Equation Lyapunov Function Function Versus Invariant Manifold Lyapunov Function Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. M. Tkachuk
    • 1
  1. 1.Shevchenko Kyiv UniversityKyiv

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