Milnor attractors and period incrementing on pattern iterations of flat top tent maps - Silva, Luís; Silva, Teresa M. (Topological Methods in Nonlinear Analysis, 2025)
In this paper, we consider the family of non-autonomous dynamical systems obtained by iterating tent maps with a flat top of constant value u introduced at instants i such that s_i=0, where s is a binary sequence that we call the iteration pattern. We introduce symbolic dynamics and study the kneading invariants for these dynamical systems. More precisely, we define the kneading invariants K(u,s) as symbolic sequences and study sufficient conditions for a symbolic sequence to be a kneading invariant K(u,s) for some u, for each iteration pattern s. Finally, we describe the parameters u for which there are Milnor attractors for iteration patterns s such that s_np=0 for all n, as limits of parameter sequences corresponding to local attractors, organized according to a period-incrementing structure.