Dynamical Systems with Convex Lyapunov Functions
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.
KeywordsBanach Space Natural Number Lyapunov Function Convex Subset Open Neighborhood
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