On the predictability of discrete dynamical systems (Q2782625)

The author shows that most functions in the set \(H(X)\) of all homeomorphisms from a metrizable compact topological \(n\)-manifold \(X\) onto \(X\) (\(n\geq 1\)) are nonsensitive at most points of \(X\). When \(B^n\) is a closed unit ball of \(R^n\) and \(n\geq 2\) it is proved that for most functions in \(H(B)\), the set of all nonwandering points has Lebesgue mesasure zero and that most points from the set of nonwandering points are recurrent and non-periodic.