Weak mixing and chaos in nonautonomous discrete systems

Strong mixing measures and invariant sets in linear dynamics

“…This fact contrasts with the case of nonautonomous interval maps, where it was shown that there are examples which are weakly mixing of order 2 which are not weakly mixing of order 3 as it is shown in Theorem 9 in [4], but once an interval NDS is weakly mixing of order 3, then it follows immediately that it is of arbitrary order n ≥ 2 as it is proved in Theorem 11 in [4].…”

“…In the last chapter, motivated by the work of Balibrea and Oprocha [4], where they obtained several results about weak mixing and chaos for nonau…”

“…En l'últim capítol, motivats pel treball de Balibrea i Oprocha [4], on van obtenir resultats sobre propietats mesclants i caos per a sistemes discrets no autònoms en conjunts compactes, estudiem propietats mesclantes per a sistemes dinàmics lineals no autònoms sobre certs subconjunts invariants. Tots els resultats d'aquest capítol han sigut publicats en [87].…”

“…Our work has its starting point in [4], where Balibrea and Oprocha obtained several results about weak mixing and chaos in nonautonomous discrete systems on compact sets. Some of their results will be used to induce the corresponding dynamical behavior on linear nonautonomous systems.…”

“…We will essentially follow the notation of [4] and we will denote a NDS as (X, T ∞ ). These notions can be extended naturally to a system (X, (T k ) k ) of sequences of maps T k : X → X, k ∈ N, by substituting T (k) by T k .…”