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Dynamical Systems with Convex Lyapunov Functions

  • Simeon Reich
  • Alexander J. Zaslavski
Part of the Developments in Mathematics book series (DEVM, volume 34)

Abstract

In this chapter we consider a complete metric space of sequences of mappings acting on a bounded, closed and convex subset K of a Banach space which share a common convex Lyapunov function f. We introduce the concept of normality and show that a generic element taken from this space is normal. The sequence of values of the Lyapunov uniformly continuous function f along any (unrestricted) trajectory of such an element tends to the infimum of f on K. We establish a convergence result for perturbations of such trajectories. We then show that if f is Lipschitzian, then the complement of the set of normal sequences is σ-porous.

Keywords

Banach Space Natural Number Lyapunov Function Convex Subset Open Neighborhood 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Simeon Reich
    • 1
  • Alexander J. Zaslavski
    • 1
  1. 1.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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