2024/05/21 by Cobollo, Ch., Peris, A.
#26A18 #37B02 #46B20 #47A16 #47B37 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2405.12626
The notion of disjoint A-transitivity for a Furstenberg family A is introduced with the aim to generalize properties derived from disjoint hypercyclic operators. We begin a systematic study by showing some of the basic properties, including necessary conditions to inherit the property on the whole space from an invariant linearly dense set containing the origin. As a consequence, we continue the study of the link between non-linear and linear dynamics through Lipschitz-free spaces by presenting some necessary conditions to obtain disjoint A-transitivity for families of Lipschitz-free operators on F(M) expressed in terms of conditions in the underlying metric space M.