2023/03/16 by Mohammad Salman, Salman, Mohammad, Ruchi Das +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2303.09579
openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the concept of multi-sensitivity with respect to a vector for a non-autonomous discrete system. We prove that for a periodic non-autonomous system on the closed unit interval, sensitivity is equivalent to strong multi-sensitivity and justify that the result need not be true if the system is not periodic. In addition, we study strong multi-sensitivity and N-sensitivity on non-autonomous systems induced by probability measure spaces. Moreover, we first prove that if fn converges to f uniformly, then strong multi-sensitivity (respectively, N-sensitivity) of the non-autonomous system does not coincide with that of (X, f). Then we give a sufficient condition such that non-autonomous system is strongly multi-sensitive (respectively, N-sensitive) if and only if f is so. Finally, we prove that if a non-autonomous system converges uniformly, then multi-transitivity and dense periodicity imply N-sensitivity.