On the predictability of discrete dynamical systems II
Nilson C. Bernardes · Proceedings of the American Mathematical Society · 2005
Given a metrizable compact topological n n -manifold X X with boundary and a metric d d compatible with the topology of X X , we prove that “most” continuous functions f : X → X f : X \to X are non-sensitive at “most” points of X X but are sensitive at every point of an infinite set which is dense in the set of all periodic points of f f . We also establish some results concerning sets of periodic points and non-wandering points.