Motivated by recent studies on the notions of lineability and spaceability in the context of linear dynamics, in this talk we shall investigate the “vastness” of chaotic phenomena in the context of linear operators, with a special focus on composition operators. Chaos will be analyzed both, in the classical sense of Baire and in terms of lineability and spaceability. In this walk through the investigation of topological and linear sizes of chaos, we shall also present, in the context of composition operators on Lp spaces, 1 ≤ p < ∞, with dissipativity and bounded distortion, recent characterizations of weakly mixing and frequent hypercyclicity. As a consequence, parallel results will be deduced for fundamental mathematical objects: bilateral weighted backward shifts on lp spaces.
Martina Maiuriello
Università degli studi della Campania Luigi Vanvitelli
